The 25-year-old was hurt on Oct. 12 in Game 4 of the AL Division Series at the Chicago White Sox when he tried to make a leaping catch at the wall on Gavin Sheets' second-inning home run.
Meyers had hoped to return later in the postseason but did not play again. He was 3-for-8 with two RBIs against the White Sox.
Houston said Meyers is not expected to be ready for game competition before opening day.
Meyers started the season at Triple-A Sugar Land, made his big league debut on Aug. 1 and hit .260 in 49 games with six homers and 28 RBIs.