Police believed he was planning a similar attack to those carried out in France and Belgium in November 2015 and March 2016.
German Interior Minister Thomas de Maiziere said: "According to what we know, the preparations in Chemnitz are similar to the preparations for the attacks in Paris and Brussels".
He said al Bakr had links to Isis.
Three others were arrested in connection with the plot, one in Chemnitz city centre and two others at the railway station.
Terrorism in 2016: Terror attacks in Europe claimed by Isis
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It comes amid growing anger about Chancellor Angela Merkel's "open door policy" towards refugees.
Over the summer there were a number of attempts by Syrian asylum seekers to attack targets in Germany – including a failed asylum seeker who blew himself up outside a music festival after failing to get inside and an Afghan teenager attacking train passengers with an axe in Würzburg.
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