The 26-year-old, a recent transfer target for Leeds, had agreed a move to the Midlands after the Glasgow club accepted a fee reportedly in the region of £250,000.
Wolves boss Mick McCarthy said: "Alan has gone back to Rangers. We'd agreed everything with him but something has shown up in the medical which we are not completely happy about.
"It's nothing serious, it's something bio-mechanical but that's something for Alan and Rangers to sort out, not us. He's a good player who would have added to the squad but that's not going to happen. In a way this is a credit to our medical team and how thorough they are."