The man was held on suspicion of using words or carrying out behaviour likely to stir up racial hatred in connection with comments made on a social media site about the centre. He is currently on police bail as inquiries continue.
Police have also confirmed they are carrying out a full investigation into complaints about alleged offensive and racist comments made on a Facebook page regarding the prayer centre, which is being planned for Column Lodge in Preston Street.
The arrest was made last Thursday, but only made public this afternoon.
Supt James Tozer said this afternoon: "We are working closely with community groups to prevent any escalation regarding this matter and in particular, the local Muslim group who intend to use the centre as a prayer room and community centre.
"They have had a local prayer room here in Shrewsbury for the last ten years and they are a welcome and well established part of our community."