The former Croatia international has suffered with the problem throughout the season, restricting him to just 19 Premier League starts in 2014-15.
Jelavic has scored eight goals in that time, and has recently struck up a useful partnership with January signing Dame N'Doye.
However, Thursday's announcement means Jelavic is unlikely to return before May, although he could make his comeback for Hull's run-in as they look to avoid the drop down to the Championship.
"The club's medical staff had hoped to manage Jelavic's knee through until the end of the season, however, following the Leicester game [last Saturday] it was decided surgery should take place as soon as possible to prevent further damage and complications in the future," a Hull statement read.
"Jelavic will now undergo a period of rehabilitation in his bid to regain fitness."
