The 30-year-old scored his 100th career goal in Rangers' 1-1 draw against Nottingham Forest on Sunday, but had to be substituted at half-time after suffering a recurrence of the problem which sidelined him recently.
Smith is definitely ruled out for Saturday's trip to Preston and boss Neil Warnock admits he will be missed.
"It's the same hamstring so it's probably a couple of weeks, it won't be long," said Warnock.
"The way he took his goal was superb and I thought he looked a real threat so I was disappointed to see him go off.
"We didn't have enough nous after he went off, he was they key for us."
Source: PA
Source: PA