Collins was forced off in 's 1-1 draw against in the Premier League last weekend with the injury.
Bees boss Keith Andrews confirmed in his news conference before their game against that the centre-back is set for a spell on the sidelines.
"No, he won't be involved this side of the international break. Unfortunately, he's picked up a calf injury," Andrews said when asked about the defender, who has 40 international caps.
"He probably felt it a little bit earlier in the game and tried to play through it, naturally, like he would, given the type of character he is and being one of our leaders and our captains.
"So, no, unfortunately he won't be involved. "
Heimir Hallgrimsson's side open their Group B3 campaign away to Kosovo on Thursday, 24 September before facing Israel three days later.
The Irish then host Austria at the Aviva Stadium on Thursday, 1 October and close the extended international break when they take on Israel again at a neutral venue on Sunday, 4 October.
