Palmeiro, who played with the Rangers from 1989-93 before re-signing as a free agent during the off-season, also had surgery on the knee on Feb. 10.
He was working out with the club and had been expected to return by the end of the week, but reinjured his knee while jogging Thursday. Dr. John Conway operated on the knee Sunday at Fort Worth, Texas.
Palmeiro, 34, has appeared in 1,368 games in the '90s, second to Cal Ripken Jr. He has not missed more than three games in a season since 1990.
Texas said there is an outside chance he could be ready for opening day.
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