The mayor of the city called it an "attack" motivated by "hate", but police have remained cautious about naming the killer's motives.
Here is what we know about the attack so far.
What happened?
Around 3:10 pm (1310 GMT), a man carrying a large knife entered the supermarket belonging to the Edeka chain on Fuhlsbuettler Strasse, a lively shopping street in the Barmbek district of northern port city Hamburg.
He struck out wildly at people around him, killing one man and wounding five others.
Eyewitnesses said the man shouted "Allahu Akbar" (God is greatest) as he ran out of the supermarket, pursued by passers-by armed with chairs and other improvised weapons.
One of the group was hurt while they were overpowering the attacker, who was then arrested by police.
Who was hurt?
Police have identified the dead man as a 50-year-old believed to be a German citizen.
Those hurt in the supermarket included a 50-year-old woman and four men aged 19 to 64, while a 35-year-old Turkish man was wounded while capturing the attacker.
All of the injured are being treated or operated on in hospital, some of them with serious injuries, police said.
Who was the attacker?
The attacker was a 26-year-old man born in the United Arab Emirates, but police have yet to confirm his nationality.
He lived in a migrant accommodation centre in Hamburg, which was searched by heavily armed police late Friday according to newspaper Bild. He supported himself with "odd jobs," German media reported.
Hamburg mayor Olaf Scholz said that the man was a failed asylum seeker whose deportation had been delayed because he had no papers.
His asylum status matches that of Anis Amri, who killed 12 people with a truck at a Berlin Christmas market on December 19.
Islamist connection?
Police have not commented on a possible motive for the crime, saying only that they are "continuing to investigate every possibility".
But multiple German media reported that the man was known to the authorities as an Islamist and that police were investigating his connections to Germany's Salafist scene.
Scholz called his actions an "attack" in which he had "turned his hatred against us".
Citing security sources, news website Spiegel Online reported that the suspect suffers from mental health problems and regularly takes drugs.
Overpowered
A group of passers-by tracked the killer as he fled the supermarket with bloody knife in hand.
Amateur video footage showed them circling him in the middle of a busy city street, hurling chairs to keep him at a distance as he brandishes his knife and yells.
A 35-year-old Turkish man finally managed to overpower him using a pole, Spiegel Online reported, suffering injuries himself in the process.
Police then arrested the attacker.
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