Burns required lengthy pitchside treatment at Seaview in the 1-1 draw with Crusaders before moving to Belfast’s Royal Victoria Hospital on Saturday.
On Sunday, Glentoran posted the following message on the club website: “The club is pleased to report that Bobby underwent successful surgery this afternoon for the injuries he incurred at Seaview yesterday afternoon and that he is now on the road to recovery.
“Everyone at the club and the entire Glentoran family wish Bobby all the best for a speedy recovery and return to action.
“Best wishes Bobby.”
Glens boss Warren Feeney told BBC Radio Ulster following Saturday’s game: “I went in to see him, he’s not in a good way the kid.
"He spoke to me but it’s not a good sight to see what he’s got around him at this minute, so we’re going to take him straight to the Royal.
"But I must say a big thanks to the St John Ambulance and Crusaders for the way they’ve treated and looked after him.
"Our prayers are with Bobby at this moment, we hope it’s not too bad.
“But what we’re hearing...it could be a few months.”