Twelve people died in the 19 December attack. Amri fled to Italy and was shot dead by police in Milan.
Investigators believe Bilel A, aged 26, was either involved in planning the attack or at least knew about it.
Police say they have arrested him on suspicion of benefit fraud as they do not have enough evidence against him.
Federal prosecutors' spokeswoman Frauke Koehler told reporters on Wednesday that the suspect had known Amri since the end of 2015 and that the pair had met at a restaurant on the evening before the attack and had "very intense conversations".
The suspect's home in an asylum shelter had been searched and communication devices taken away for analysis, she added. The man is believed to have used at least two false names in several German cities between April and November 2015.
A former flatmate of Amri's is also being investigated as a potential witness. Amri twice tried to contact him on 19 December, although it is unclear whether or not they spoke.
Over a fortnight after the attack, German prosecutors have said there is now no doubt that 24-year-old Anis Amri was behind the attack.
And investigators across Europe have a clearer picture of what happened on the night of the attack and how Amri fled south to Italy. Police in Italy confirmed on Wednesday that the gun used by Amri to murder Polish driver Lukasz Urban was the same he fired four days later in Milan.
Shortly before the attack, Amri is thought to have gone to Friedrich-Krause-Ufer, a street where he shot dead Mr Urban. He then went to a mosque and returned to the lorry to carry out the attack on Breitscheidplatz a few miles away.
Amri was then seen on camera a short distance from the square at Zoo station, raising an index finger, a gesture linked to jihadist group Islamic State. What happens next is unclear, but it is thought that he escaped to the North Rhine-Westphalia area of western Germany.
His final journey took him through the Netherlands, Belgium, France and Italy, exploiting the open borders of Europe's Schengen zone.
Some of Amri's story is yet to emerge. Swiss police said they too had opened an inquiry into the Berlin attack after receiving information from another police force.
Berlin police have detained a Tunisian man suspected of eating dinner with Anis Amri the night before he drove a lorry into a crowded Christmas market.