General manager Jeff Luhnow said the procedure was to remove loose bodies in Bregman's elbow. Luhnow said the All-Star Game MVP will be limited during spring training, but Bregman is optimistic he'll be able to start playing in games in early March.
"I'll be ready ... believe that," Bregman wrote on Twitter.
Bregman, 24, hit .286 last season with 31 home runs, 103 RBIs, 105 runs, 96 walks, 51 doubles and a .926 OPS -- all career highs.
He told MLB.com on Friday that his right arm had been "bugging me" since 2016 and that it locked up last month. A CT scan revealed bone chips were the cause.
"It's something you can play through a little bit, but when it locks out, you're looking at a DL stint, and I wasn't willing to risk going on the DL this year for something I know I could fix before the season started," Bregman told MLB.com. "So we went ahead and knocked it out."
The second overall pick in the 2015 amateur draft, he has hit .282 with 58 homers and 208 RBIs in his two-plus seasons with the Astros.
The Associated Press contributed to this report.