Santa Cruz to miss start of season
"We're hoping by the end of the month he'll be available," manager Mark Hughes said on the club's website.
"I'd rather give him the time that he needs."
The Paraguay striker has been struggling to make a full recovery from knee surgery he had in April. He joined City from Blackburn Rovers in June and has missed all the team's pre-season games.
City start their Premier League campaign on Saturday with a trip to Blackburn.