Authorities have said the prayer house, formerly known as the al-Quds mosque, was a meeting and recruiting point years ago for some of the September 11 attackers before they moved to the US.
Mohamed Atta, leader of the September 11 attackers, as well as Marwan Al-Shehhi and Ziad Jarrah had studied in Hamburg and frequented the mosque.
Reschreiter said Monday marked the first time the mosque had been closed, and that it had been under observation by local intelligence officers for "quite a long time".
A 2009 report by the Hamburg branch of Germany's domestic intelligence agency also said the mosque had again become the "centre of attraction for the jihad scene" in the northern port city.
It said some people who belonged to the mosque's cultural association and prayed there had travelled to an armed training camp in Uzbekistan.
A group of 11 people that visited training camps in Uzbekistan in March 2009 was formed at Taiba mosque, the report said.
Most of the group's members were either German converts, of Middle Eastern origin or from the Caucasus region.
"A very important factor for the radicalization of the group members was certainly their joint visits to the mosque," the intelligence report stated.
It appears that one man from the group joined the Islamic Movement of Uzbekistan, an armed group in Central Asia, the report said.