It was rescheduled for 4:19 p.m. Monday. The teams will lose their travel day, and the series is then slated to resume with Game 3 on Tuesday in Detroit.
Texas beat Detroit 3-2 in Saturday night's opener, a game delayed twice by rain in the top of the fifth inning — first for 41 minutes and then for 1:09.
More rain was predicted in the area for Sunday night.
"We felt with the forecast that we had that we didn't want to experience what we did last night. … With the forecast for this evening, it appears that it's going to be a duplication of what we saw," Rangers president Nolan Ryan said Sunday. "The one thing we're concerned about is the integrity of the game and not put either team in a situation where there is a possibility the elements could affect the outcome of the game."
The rain delays Saturday night were the first at Rangers Ballpark since May 24. This season was played during one of the hottest and driest summers in North Texas, including 27 games when the temperature was 100 degrees or more at first pitch.
After the postponement, Tigers manager Jim Leyland said Magglio Ordonez will miss the rest of the postseason because of an ankle injury, the second Detroit Tigers outfielder out of the ALCS.
Leyland said Ordonez is having problems with the right ankle that he broke last season, an injury that caused him to miss more than a month this summer.
Ordonez came out of Saturday's opener after the second of two rain delays in the top of the fifth inning. Ordonez drew a walk during a short resumption of play between the delays and was replaced by a pinch-runner when the game resumed for good.
Delmon Young was taken off the roster Saturday because of an oblique injury.