The 37-year-old sustained the problem during Saturday afternoon's 2-2 draw with Burton Albion.
"It's frustrating for us and him," manager Mark Yates told BBC Gloucestershire. "At least we're not playing Saturday and Tuesday too much too often.
"He'll be a bad patient because all he wants to do is play. We've just got to keep him wrapped up and make sure we do everything we can to make sure he's back as quick as he can."
Cureton signed on at Whaddon Road earlier this summer following his release by Exeter City.