A 2-0 third round replay win at the Ricoh Arena on Tuesday earned City a fourth round clash against Middlesbrough, but came at a cost for the West Country side.
Jevons suffered ankle ligamanet damage, and the club's top scorer is expected to be out of action for a minimum of two weeks.
He is likely to sit out the league clashes with Oldham and Brighton, as well as the glamourous visit of Boro in the Cup.
"Jevo has torn his ligaments in his ankle and will be out for around a couple of weeks," Robins manager Gary Johnson told PA Sport.
"It will be touch and go whether he plays again this month because he is usually a quick healer but we will have to wait and see."