Captain Walter Barrie, 41, an avid fan of the Ibrox club, was serving in Afghanistan with The Royal Scots Borderers when he was shot in Helmand province.
The manager said: "On behalf of all the players, directors and management team I would like pass on my sincere condolences to Captain Walter Barrie's family.
"Everyone at the club is thinking about them at this difficult time.
"He was held in the highest regard by all who knew him and his loss will be felt by the football club as well."
The Ibrox club said Walter, from Lanark, was a "huge" supporter who had helped organise morale-boosting matches between troops in Helmand.
Mr Barrie, who is survived by wife Sonia and son Callum, was the latest victim in a series of attacks in which Afghan military or police have turned their weapons on British troops working alongside them.
Rangers players are expected to wear black armbands in memory of the soldier when they play their Third Division league match against East Stirling, on Saturday at lunchtime.