The 21-year-old, who joined the Central Park side on a season-long loan arrangement in July, was missing from the Blue Brazil's 3-0 win over Queen's Park at Hampden.
A spokesperson for the Fifers confirmed the Pole would be missing "for a few weeks" with the injury. Motherwell youngster Peter Morrison, who signed a seven-day loan deal, deputised in the win over the Spiders.
Dabrowski is yet to make his senior debut for Hibs despite making the bench on 31 occasions. He has had previous loan spells at Civil Service Strollers and Berwick Rangers.
The former Lech Poznan youngster has won plaudits for his performances between the sticks for Gary Bollan's side, keeping three clean sheets in 11 matches.
It's not the first serious injury the shot-stopper has suffered. Just a week into his time with Hibs, initially on loan, he damaged his thumb during training to the extent he required stitches and surgery.