The Lancashire batsman had four stitches in a head wound and was also treated for a cut hand.
Fairbrother should play in Wednesday's opening World Cup match against New Zealand at Ahmedabad but the England doctor, Philip Bell, will keep a close eye on his first real patient of the tour.
Wayne Morton, the physiotherapist, remains pleased with Robin Smith's rate of recovery from a groin injury, while Dominic Cork's knee problem has all but disappeared.
England established that replacements for "genuinely" injured players will be allowed throughout the World Cup.
England's four official reserves are Mark Ramprakash, Dermot Reeve, Mike Watkinson and Angus Fraser.Reuse content