The midfielder suffered a hamstring injury during the first half of his club's 2-1 friendly victory at Broadwood Stadium.
Smith said: "It is disappointing but the initial assessment from the medical team is that it isn't too major and it might just be two or three weeks that he's out for.
"It's unfortunate having gone through a pre-season to get something like that, and he has been playing well too, so that's the disappointing thing."
While Rangers suffered a blow over Fleck, they were able to welcome back Andrius Velicka after almost a year on the sidelines following cruciate ligament damage.
The former Hearts striker came off the bench at half-time and he is hopeful he can be part of Smith's team on a regular basis following the departures of Kris Boyd and Nacho Novo.
"It's amazing," said the Lithuanian, who suffered his knee injury at the start of a loan spell with Bristol city.
"I am just so happy to be back on the park and to be playing for Rangers.
"Right now I feel so happy and very strong but I know I need to stop myself getting too excited. The tiredness will come because it is so long since I played.
"If I can get back to 100% fitness I think there will be a chance to play, but now I just need to be patient.
"I need to keep training and to have some more games to make sure I am getting fitter all the time."
First-half goals from Steven Naismith and Kenny Miller gave Rangers victory although John Stewart pulled one back early in the second half after Smith had made several changes.
The Rangers manager handed starts to Jordan McMillan and Jamie Ness, with 10 players from the youth ranks involved at some stage.
Smith, who saw Sasa Papac return following a knee injury, added: "There was some good movement from us in the first half and two good goals and in the second period it was good to see some of the young lads get a run-out.
"We had a bit of a dip at the start of the second half but that happens in these games when you make changes. And once they settled down I thought they did well."