The mosque on Perleberger Strasse is connected to the Fussilet 33 association, which has been under police surveillance because of alleged attempts to recruit new ISIS members.
The three men, aged 21, 31 and 45, are formally suspected of having prepared “a serious act of violent subversion” for planning to attend combat training.
A police spokesman said there was no indication of any concrete plan to carry out an attack in Germany.
He said the men were planning to travel to the Middle East for combat training.
German newspaper Bild reported the three suspects had close links to ISIS members in Syria and Iraq and were frequent visitors of the mosque in the Moabit district of the German capital.
Police forensics teams have conducted fingertip searches of the controversial mosque where Amri worshipped.
The Tunisian immigrant killed 12 people when he drove a stolen lorry into the a Christmas market in Berlin on December 19 in the worst of a spate of attacks on random members of the public in Germany over the past year.
He was shot dead after a shoot-out with police in Milan four days later.