Dodgers manager Dave Roberts said the operation will be performed Friday in Los Angeles.
"It's a big blow," Roberts said. "We just feel for Corey. It's something that he's had to deal with for a couple of years. The elbow finally gave way, and I feel bad for him."
Said Seager, "I was pretty good through spring, and pretty good through the beginning, but then -- like I said -- this weekend I had a few bad throws that really irritated me.
"In the physical sense, it hurt, had some numbness, and it was time to go get it looked at."
Seager said he was "hoping for inflammation" when he went in for the MRI.
"It was hurting worse, but I couldn't tell if that was just from how recent it was," Seager said. "You obviously don't hope for what it turned out to be, but I was hoping for inflammation."
Seager, the 2016 NL Rookie of the Year and a two-time All-Star, had two home runs, 13 RBIs and a slash line of .267/.348/.396 in 26 games this season.
He previously missed just one game in 2018, a March 31 win over the Giants.
Roberts said Chris Taylor would move in from the outfield to become the everyday shortstop.
Los Angeles recalled Breyvic Valera from Triple-A Oklahoma City to replace Seager on the roster.
Information from The Associated Press was used in this report.