Brosque suffered the injury during last week's 1-1 draw with Melbourne Victory at AAMI Park.
The 32 year-old will now miss crucial matches against Pohang Steelers in the Asian Champions League as well as potential do-or-die clashes against Brisbane Roar and Adelaide United.
Brosque could be back for the ACL clash with Urawa Red Diamonds on April 20, and could play a part in Sydney's finals campaign should they make it.
Head Coach Graham Arnold said: “It’s a big blow. At the start of the year when we did our recruitment I was looking for Alex Brosque to be a key figure and one of our main goalscorers.
“He has missed 14 games so far this season and as our leader and captain it’s a big blow. We now need everyone else to step up and fill his shoes.”
The strain is new injury for the Sky Blues striker and Brosque will undergo close work with club medical staff to ensure no future issues.