The 23-year-old sustained the ankle injury during last weekend’s goalless draw at Annan.
“David has obviously got a very sore one,” said Rangers boss Ally McCoist.
“The good news is that it’s not broken.
“He has been for an X-ray but there is massive swelling and there looks to be a good bit of damage to the ligaments unfortunately.
“We are waiting on the swelling going down and then David will get a scan in the next few days.”
Templeton signed a four-year contract when he joined Rangers from Hearts at the end of August.
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