The unidentified attacker used a "stabbing weapon" in the assault around 6:00 pm (1700 GMT), said police.
The victim is stable following emergency surgery, police added later.
Six people who witnessed the assault received counselling from rescue services who rushed to the scene, where bloodied clothes were left on the ground.
Police, some with assault rifles, cordoned off the Memorial to the Murdered Jews of Europe, a sombre grid of concrete steles located near the Brandenburg Gate.
With the downtown area doused in blue police lights and sirens wailing, police launched a manhunt of the inner city and used a cherry picker crane to get a birds-eye view of the vast memorial.
Then, over three hours after the assault, a man approached a group of police at the scene before the officers wrestled him to the ground, AFP journalists witnessed.
"We have the suspect," shouted one officer as other police rushed over. The man was handcuffed lying face-down on the ground.
"We just arrested a male suspect," police spokesman Florian Nath soon confirmed. "It's probably the suspect that attacked the 30-year-old Spanish citizen at 6:00 pm here at the memorial."
Nath said the man detained had been seen by police to have "blood on his hands".
Police stressed that so far "we don't know anything about the motive" or the identity of the suspect in custody, who was refusing to talk to them.
Spate of attacks
The assault came two days before national elections and after a series of deadly attacks, including car-rammings and stabbing sprees, that have shocked Germany.
German police said earlier Friday they had arrested an 18-year-old Russian man on suspicion of planning a "politically motivated" attack in Berlin.
He was detained late Thursday in the state of Brandenburg, which surrounds Berlin, police and prosecutors said in a statement.
Authorities did not provide further details about the alleged attack plot, but the Tagesspiegel newspaper reported the suspect was Chechen and was believed to have been planning an attack on the Israeli embassy.
Riot police and specialist officers were involved in making the arrest, which came after a tip-off, officials said.
Germany has grown increasingly alarmed about rising anti-Jewish sentiment since the October 7, 2023 Hamas attack on Israel that sparked the war in Gaza.
A record 5,164 anti-Semitic crimes were recorded in 2023, compared with 2,641 the previous year, according to figures from the domestic intelligence agency.
In an attack in early September, German police shot dead a young Austrian man known to have had ties to radical Islam as he was preparing to carry out an attack on the Israeli consulate in Munich.
In December a man drove an SUV at high speed through a Christmas market crowd, killing six people and wounding hundreds in the eastern city of Magdeburg.
In January a man with a kitchen knife attacked a kindergarten group, killing a two-year-old boy and a man who tried to protect the toddlers.
Another major attack followed just 10 days before the election, when a man ploughed a Mini Cooper car through a street rally in Munich, killing a two-year-old child and her mother and wounding dozens.
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