Isis-affiliated news agency Amaq reported on Saturday that the jihadist group had claimed responsibility for the October 16 knife attack.
"A soldier of the Islamic State stabbed two individuals in Hamburg city on the 16th of this month," the release said, in response to "calls to target the citizens of coalition countries" that are fighting Isis in Iraq and Syria.
"We are looking into the authenticity of the IS claim of responsibility," the police spokeswoman told AFP.
A specialist political crimes unit is now involved in the case, she added.
Meanwhile, news agency DPA reported on Sunday that German federal prosecutors had "taken note" of the claim and may take over the case from regional authorities.
Hamburg police reported a knife attack on the banks of the Alster river on the 16th.
One victim, a 16-year-old boy, was fatally wounded, while a 15-year-old girl who was with him escaped unharmed after the attacker shoved her into the water.
Police launched a dragnet but never found the man, described as aged 23-25 and of "southern" appearance.
"The motive for the crime is unknown and is the subject of further investigation," the October 17 police statement said.
The group's claim of responsibility included no further details about the attack or the perpetrator.
The German air force is participating in the anti-Isis bombing campaign in Iraq and Syria with in-air refuelling and reconnaissance flights.
Germany has so far escaped a major terrorist attack by IS along the lines of those carried out in neighbouring France and Belgium, although it has foiled several plots and suffered numerous attacks by individuals.
A teenage girl is currently on trial in Hanover after wounding a police officer with a knife in February, with prosecutors arguing Isis is behind the attack.
In July, Isis claimed it was behind a suicide bomb attack that wounded 15 people as well as an axe attack in a train by a teenage asylum seeker that left five people hurt.
June saw a group of men arrested on suspicion of planning a bomb attack on western regional capital Duesseldorf, while another suspected bomb-maker was arrested in eastern Saxony state in October but later killed himself in his cell.
Previously, a 41-year-old Iraqi was killed by police after wounding an officer in Berlin in September 2015.
A month before, two German jihadist fighters claiming to belong to Isis in Syria released a video in which they threatened Germany and Chancellor Angela Merkel.