The video was released through the jihadi organization's news agency Amaq, which had claimed a link earlier in the day.
The assault on a regional train near the southern city of Würzburg on Monday left two of the victims in a critical condition, said Joachim Herrmann, the interior minister of Bavaria state. The teenage assailant was killed as he tried to flee.
David Thomson, an Isis expert at French radio station RFI tweeted that "to prove the link the agency Amaq has released a video of the German train attacker."
The video released by Isis's affiliated Amaq news agency, subtitled in Arabic, shows teenager "Mohammed Riyadh" - knife in hand - announcing in Pashto he would carry out an "operation" in Germany, and presenting himself as a "soldier of the caliphate".
The Bavarian interior minister Joachim Herrmann had said at a press conference in Munich earlier on Tuesday that there is “no indication” of a link between the teenager and Isis.
At the same time, he gave details of how investigators had found a self-made Isis flag in the teenager's bedroom and a text, partly in Arabic script and partly in Latin script, which suggested that “he could have radicalized himself” said Herrmann.
On Tuesday morning, terror group Isis claimed responsibility for the axe attack.
The group said that the attack was carried out by one of its "soldiers", according to French newspaper Le Figaro.
Thomson of RFI tweeted that they had taken responsibility for the attack.
The Amaq statement claims that the 17-year-old Afghan who carried out the attack had "executed the operation in response to calls to target nations in the coalition fighting the Islamic state."
Thomson tweets that this is the first attack in Germany that has been claimed by Isis.
A hand-painted Isis flag had earlier been found among the belongings of the 17-year-old who attacked train passengers with an axe and a knife on Monday, the Bavarian interior minister said.
“It is not at all surprising that Isis have taken responsibility for this attack,” Dr. David Arn, an expert on Isis at the Ludwig Maximilian University in Munich told The Local on Tuesday.
“It is currently ‘en vogue’ for Isis to take responsibility for the actions of so-called ‘lone wolves’”, he said, adding that this attack seemed to be “exactly the same phenomenon” as the more fatal rampages in Nice and Orlando.
It is unlikely that Isis had any role in coordinating these attacks, he argues, saying that they appear to be the actions of people acting alone who use the call to jihad as an excuse for their crimes.
Arn also warned that Isis are seeking to use the “explosive potential” in this crime to exploit tensions among Muslims and non-Muslims in Europe.
'Like a slaughterhouse'
"We hope that those who were gravely injured make it," Herrmann told ZDF public television.
The assailant had arrived as an unaccompanied minor in Germany, Herrmann said. A hand-painted flag of the Islamic State group was found among the belongings of the Afghan refugee, who had been staying with a foster family in the region.
"It is quite probable that this was an Islamist attack," said a ministry spokesman, adding that the assailant had shouted "Allahu akbar" (God is greatest).
However he stressed that the investigation was ongoing and that the teenager appeared to have acted alone.
The assault happened around 9:15 pm on the train which runs between the town of Treuchlingen and Wuerzburg in Bavaria.
An eyewitness who lives next to the railway station told DPA news agency that the train, which had been carrying around 25 people, looked "like a slaughterhouse" with blood covering the floor.
The man, who declined to give his name, said he saw people crawl from the carriage and ask for a first-aid kit as other victims lay on the floor inside.
"The perpetrator was able to leave the train, police left in pursuit and as part of this pursuit, they shot the attacker and killed him," a police spokesman said.
Herrmann later said that the teenager was shot when he attacked police while trying to escape the scene.
A special police force unit happened to be nearby and was able to mobilise quickly, Herrmann added.
The four seriously injured victims are members of a family from Hong Kong, authorities in the southern Chinese city said Tuesday, adding the immigration department was providing them with assistance.
Germany has thus far escaped the kind of large-scale jihadist attacks seen in the southern French city of Nice last week, in which 31-year-old Mohamed Lahouaiej Bouhlel used a truck to mow down people leaving a Bastille Day fireworks display, killing 84 people. The attack was claimed by the Islamic State group.
In May in Germany, a mentally unstable 27-year-old man carried out a knife attack on a regional train in the south, killing one person and injuring three others.
Early reports had suggested he had yelled "Allahu akbar" but police later said there was no evidence pointing to a religious motive. He is being held in a psychiatric hospital.
In February a 15-year-old girl of Turkish origin stabbed a policeman in the neck with a kitchen knife at Hanover train station in what prosecutors later said was an IS-inspired attack.
Police in April arrested two 16-year-olds over an explosion that wounded three people at a Sikh temple, in what was believed to be an Islamist motivated attack against an Indian wedding party at a temple in the western city of Essen.
Germany let in a record nearly 1.1 million asylum seekers last year, with Syrians the largest group followed by Afghans fleeing ongoing turmoil and poverty in their country.
However the number of refugees arriving in Germany has fallen sharply as a result of the closure of the Balkans migration route and an EU deal with Turkey to stem the flow.
Bavaria is governed by the Christian Social Union (CSU), sister party to Chancellor Angela Merkel's conservative Christian Democrats, which has been loudly critical of Merkel's welcoming stance toward asylum seekers.
The split threatened the unity of the ruling coalition in Berlin and sent the government's approval ratings plunging.
It has also put wind in the sails of a right-wing populist party, Alternative for Germany, which was founded as a eurosceptic protest outfit in 2013 but now mainly rails against Islam and Germany's refugee influx.
It currently polls at around 10 percent and is represented in half of Germany's 16 states as well as the European Parliament.
Merkel's popularity has rebounded recently but the attack in Bavaria is likely to revive political tensions.