The Senegal international injured his right shoulder in Saturday's 1-1 draw with Bayer Leverkusen, which represented Hannover's fifth Bundesliga game without a win.
Although the club confirmed on Friday that Diouf had undergone successful surgery, he will now be absent for "several months".
A statement on Hannover's official website read: "Mame Diouf has been successfully operated on Friday morning on the right shoulder.
"Diouf had been injured in the home match against Bayer Leverkusen in a duel with his opponent.
"The operation was absolutely necessary to fully restore the stability of the shoulder.
"After the successful surgery Mame Diouf will have to pause for several months."
Diouf is Hannover's top scorer this season with eight goals, having managed 12 in the previous campaign.
His absence comes as a major blow to a team who are in danger of being sucked into a relegation battle following their recent poor form.
Hannover currently sit 12th, six points clear of the relegation play-off place.
