The 24 year-old suffered the injury at training on Thursday, needing to be carried from the field by two staff members with subsequent scans revealing a 2cm tear that will rule him out for an extended period.
Taggart missed five games early last season with a calf injury while his two-year stint overseas following the 2014 World Cup was blighted by groin issues.
His absence comes with Glory yet to discover their attacking mojo despite boasting a squad that features the likes of Andy Keogh and Diego Castro, having not won away from home this season.
The striker scored 12 goals for Glory last season and had already netted three times in five games this campaign, placing more pressure on the likes of Castro and Keogh ahead of their match against Wellington Phoenix on Sunday.
Wellington will be without key duo Michael McGlinchey and Andrew Durante for Sunday's match because of international duties.