McCullers, who went 10-6 with a 3.18 ERA in 2018, is expected to make a full recovery, the Astros said.
He was placed on the disabled list with elbow discomfort from Aug. 5 to Sept. 24 but returned during the final week of the season, making three scoreless appearances. He also made five playoff appearances, posting a 1.80 ERA.
McCullers, 25, is 29-22 in his career with a 3.67 ERA.
"Days are long but years are short," McCullers posted on Twitter. "I will be back better than ever, better believe that!!! Come back SZN starts now!!!"