A date for Garcia's surgery has not been set, and the Astros said that he is expected to return at some point during the 2024 season.
"That's a tremendous blow. I mean, I was praying that it was something different, something minor," manager Dusty Baker said after Houston's 6-4 win over the Mariners on Friday. "You're always afraid of that when it's in the elbow."
He was 2-2 with a 4.00 ERA in six starts this season. Last season, Garcia was 15-8 with a 3.72 ERA in 28 starts. He was second in 2021 American League Rookie of the Year voting after going 11-8 with a 3.48 ERA in 30 games (28 starts).
Garcia's injury came the same day fellow right-hander Jose Urquidy was placed on the IL with inflammation in his pitching shoulder.
It is yet another major hurdle for the Astros to deal with.
Star second baseman Jose Altuve has been out all season after breaking his right thumb in the World Baseball Classic. Veteran outfielder Michael Brantley hasn't played this year while recovering from right shoulder surgery.
Houston is also without outfielder Chas McCormick, who has been sidelined since April 15 with lower back tightness.
Baker said before Friday's game that McCormick and Brantley could join the Astros later on Houston's road trip, likely when the team goes to Southern California to face the Angels.
The Astros on Friday also added right-hander J.P. France to the taxi squad, and he's expected to be activated Saturday to make his major league debut against the Mariners.
France, 28, was drafted in the 14th round by the Astros in 2018. He is 2-1 with a 2.33 ERA through five games this season at Triple-A Sugar Land, striking out 26 and walking 11 in 19⅓ innings.
The Associated Press contributed to this report.