If the ALDS goes the full five games, the final game would be on Oct. 6, which would be exactly two weeks from Meister's fastest estimate.
Teams are allowed to alter rosters between series, so if Lowe is healthy, he could be added for a potential AL Championship Series.
Lowe said he would travel with the team and could begin throwing again on next Wednesday. Regardless, he said he would not rush back if he isn't ready to pitch at a high level.
"I'm going to do everything I can to be ready, but I'm not going to do anything to jeopardize what this team's done all year," Lowe said. "I'm not going to try to be a hero and be selfish. If I can get out there and do it, I'm going to do it. If I can't, I'll wait for it."
The injury was a freak occurrence for Lowe, who said he's never had any injury issues with his legs and was completing a workout that he does before every game.
"I've never had any hamstring problems, ever," Lowe said. "No quads, no hammies, no calves, all arm and back."
Lowe, who has a 3.80 ERA in 52 games, was expected to be one of the 25 players the Rangers would place on their roster for the ALDS. With him out, that makes room for possible additions such as Scott Feldman, Yoshinori Tateyama, Darren O'Day and Michael Kirkman.
"I will get O'Day and Tateyama some work," Rangers manager Ron Washington said. "When we get this thing wrapped up, we can get it at any time. Right now we've got to continue to win ballgames, so I'll put them in when I can."