The veteran striker was forced off after just 15 minutes of the Ladbrokes Premiership tie at Easter Road, and had to be removed from the field of play on a stretcher.
But despite Miller and the Ibrox staff hoping for a quick recovery, further investigation revealed that the injury was worse than first anticipated.
Interim Rangers boss Graeme Murty confirmed this morning that the former Scotland international was facing a ‘significant amount of time out’.
Murty added: “Unfortunately it looks as though he has a rupture of his hamstring. We were hopeful given the way he presented, and given the fact his range was okay, but once we’ve scanned it, we have seen there is significant damage in there, so we have to be more conservative in our approach with him.
“It’s a painful one for him and a sore one for the group as he is an integral part of everything that we do around the place. If anyone knows Kenny, they know the standards that he drives. So we are going to miss him.”
Miller has scored four goals in 18 appearances in all competitions this season, but was frozen out by former Ibrox boss Pedro Caixinha for much of October.
Murty also gave an update on the other injured members of his squad, revealing that Jordan Rossiter and Jak Alnwick have both had injections in a bid to clear up their respective injury problems while Ibrox skipper Lee Wallace is also close to a return.
Carlos Pena and Fabio Cardoso, who were left out of the squad to face St Johnstone, will be back in contention for Saturday’s trip to Kilmarnock.