"It looked a nasty injury at the time - the news could have been worse," boss Gary Johnson told City's website.
"The lower end of his hamstrings took a bit of a pounding, but a scan has shown no cartilage or cruciate damage."
Brooker and fellow striker Enoch Showunmi will both miss Tuesday's trip to Bournemouth.
But Showunmi may be in contention for Saturday's game with Oldham if he shakes off a virus in time.