The former Light Blues keeper was stretchered off after a collision with team-mate Alim Ozturk.
Scott Gallacher filled in between the sticks on his return to Ibrox as Robbie Neilson's side got their campaign off to a dream start.
Neilson said: "Neil took a bad one. He's got a fractured cheekbone so he'll be out for around four weeks.
"It's not great but we've got a squad and I thought that Scott Gallacher came on yesterday and did very well.
"He's a good keeper and that's the reason that we brought him in.
"I'm really disappointed for Neil but he's had a fantastic game for us. He's a leader about the place as well."
Neilson was without Soufian El Hassnoui and Callum Paterson for the Ibrox clash as goals from Danny Wilson and Osman Sow clinched a 2-1 win against their second tier title rivals.
Next up for the Jambos is the Edinburgh derby at home to Hibs on Sunday.
And Neilson will continue to monitor his crocked stars as he looks to continue Hearts' flying start to the campaign.
He said: "We've still got a couple of injuries but Soufian trained over the weekend for the first time.
"He'll join the squad in the middle of next week.
"Callum has his knee problem but that should be another three or four weeks hopefully before he's back training with the group."