The Wolves top was laid near to where the 24-year-old died following a violent street attack, in Bull Ring, just before midnight on August 15.
West Midlands Police say the suspect has been taken into custody for questioning over the theft while efforts are ongoing to trace the shirt.
Inspector Pete Sandhu, from the Dudley neighbourhood police team, said: "We’ve all felt the impact of Reece’s death which has shocked the community.
"We were in disbelief when it came to our attention that a football shirt, which had been laid in tribute to Reece, had been stolen.
"But we’ve carried out quick-time enquiries and now arrested a man on suspicion of theft.
"We’re absolutely appalled that a tribute to remember Reece, and what he meant to our community, could be stolen."
Tributes have been left outside The Clifton pub, near to where he died, which include flowers and Wolves clothing.