Crow will get a second opinion but expects to have the procedure.
"That's a big blow for him," manager Mike Redmond said Wednesday.
Crow will be the third Marlins pitcher since May -- and the 28th since 1992 -- to have the surgery, according to ESPN Stats & Information. Staff ace Jose Fernandez is still recovering and is on schedule to return around midseason.
A four-year veteran, Crow went 6-1 with a 4.12 ERA in 61 appearances last season for Kansas City but was left off the Royals postseason roster. The 28-year-old right-hander allowed two runs and six hits over eight innings during seven spring training games with nine strikeouts and four walks.
Selected by Kansas City with the 12th overall pick in the 2009 amateur draft, Crow was traded to the Marlins in November for left-hander Brian Flynn and right-hander Reid Redman. Crow is making $1,975,000 this year.
Redmond declined to announce a replacement for Crow, but Sam Dyson appears to be the most likely option.
A 26-year-old right-hander, Dyson pitched for the Marlins in parts of each of the past two seasons. He has allowed eight runs in 9 2-3 innings in spring training.
The Associated Press contributed to this report.