www.gloucesterrugby.co.uk that the fracture he suffered on Friday during the development game against Ulster will take at least four weeks to heal.
It is likely to rule him out until the end of opening month of the Premiership season, but the England seven's skipper, who led Gloucester to the Middlesex Sevens title earlier this month, was looking on the bright side.
"I would like to think I will be playing again in three or four weeks - thankfully it's not serious and I don't need surgery.
"I was at a ruck and just got trodden on - it was painful but it will not keep me out of action for too long."
Amor revealed he had returned from Gloucester's pre-season tour to at Issoire with a slight back injury and was hoping the extra time off will give him plenty of recovery time.
"I was kicked in the lower back in France and it has taken some time to recover - the extra time off at the start of the season can only do me good at this stage."