The 31-year-old is expected to be out of action for around six weeks after undergoing knee surgery.
Daly scored 21 goals last season to help the Gers win the Scottish League One title.
"It's a real shame as big Jon was fantastic for us last season," McCoist is quoted as saying by Sky Sports News. "Towards the end of the season, we would have given him a little rest if we could have but personnel indicated we couldn't.
"It looks as though he will be out for six weeks and it's a blow for the team. It's obviously a blow for him too but the bottom line is he has to get it sorted as quickly as possible."
Rangers start their Scottish Championship campaign at home to Hearts on August 10.