The 23-year-old suffered a ligament problem during training on Tuesday and the club have confirmed he will not play any part in the final 11 games of the campaign.
Sobiech, who has scored three goals in 17 Bundesliga games in 2013-14, requires surgery to repair the torn ligament.
"Artur Sobiech needs surgery after he suffered an injury to the external ligament of his left knee," said a statement on the club's official website.
"The operation will be carried out on Thursday in Cologne.
"The striker's course of treatment will be decided tomorrow.
"The Poland international will be out for a number of weeks, missing the rest of this season."
Hannover sit 11th in the Bundesliga, but are only six points clear of the bottom three after a winless four-match streak.
