Craig, who was with the Ibrox club for around 12 years from the early 1970s, is believed to have passed away in hospital on Saturday.
He was on the staff when the team won the 1972 European Cup Winners Cup against Dynamo Moscow, beating them 3-2 at the Camp Nou in Barcelona.
After leaving the club Mr Craig practised physiotherapy from his home in the South Side of Glasgow.
Mr Craig was taken to hospital after suffering a heart attack but did not recover. He is thought to have been in his early 70s.
A statement issued by Rangers said: "Rangers Football Club is deeply saddened to hear the news that former physio Tommy Craig, who was part of the backroom staff when the club won the Cup Winners' Cup in 1972, has passed away.
"Everyone at the club sends their sincere condolences to Tommy's family and friends and our thoughts are with them at this difficult time."