The 39-year-old was held by officers after the Superdry and Footlocker stores in Argyle Street were allegedly broken into.
A police cordon remained in place outside the Superdry store and an officer was guarding the scene.
Both stores were open for business.
A spokeswoman for Strathclyde Police said: "Officers were called to two incidents in Arygle Street at around 8.15am today."
Anyone with any information is asked to contact Strathclyde Police on 0141 532 2000.