The Romanian international sustained a knock to the back of his leg and limped off after just 15 minutes during the Light Blues Scottish Cup fourth round victory over Stirling Albion on Friday night.
Manager Giovanni van Bronckhorst confirmed the playmaker will now sit out the remainder of the campaign after undergoing knee surgery.
Speaking in his pre-match press conference ahead of Wednesday’s clash against Livingston, the Dutchman said: “Ianis (Hagi) needed an operation yesterday in London, so we won’t have Ianis for the season.
“He had to have a knee procedure, so that is a big blow for all of us and, of course, a huge disappointment for Ianis.
“I spoke to him this morning, he’s in a good place, he’s positive and quite focused on his recovery.
“We won’t have him available for months, so that’s the bad news for us but we look forward to welcoming him back once fully recovered.
Van Bronckhorst revealed Hagi’s absence is likely to open the door for a potential new signing in the remaining days of the transfer window.
He added: “We have an important player who is not available for the coming months, so we are looking to add a player to the squad.
“But it’s only good to bring in players who can add something to Rangers, someone we think is right and not just to make up the numbers.
“You want to have the right balance in the team, so we’re definitely looking to add a player in the coming days.
“If the right type of player doesn’t become available then you’re better to keep your squad as it is.
“It’s always a crazy time during a transfer window because you never know what’s going to happen. There’s still six days to go and we’ll just wait and see how things evolve.
“So far we have managed to keep hold of our key players and I hope it will stay like this. We need to make sure we’re prepared if anything was to happen.”