Reef had been due to play at KK's Steel Mill in Frederick Street on Saturday, April 1.
Bass player Jack Bessant, aged 52, is in hospital after suffering the injury earlier this week.
The Glastonbury-based band has also cancelled shows in Plymouth and Bournemouth in the wake of his injury.
The plan is to reschedule them as soon as possible.
Tickets will remain valid for the rescheduled dates.
"We are sorry for any inconvenience caused and are hoping that we will still be able to play the rest of the shows on this UK tour as planned," the band said on social media.
"Jack remains in hospital at this difficult time and it goes without saying that all our thoughts are with him and his family as we wish him a speedy recovery."
Reef's singer Gary Stringer is a big fan of Wolves.