Texas moved within 2 1/2 games of Boston, which lost to the Chicago White Sox, 5-1. The Rangers could not pick up more ground as they never got started. The teams will try to make it up Tuesday as part of a doubleheader beginning at 5:05 p.m.
"It's Labor Day, so we should be working," Indians manager Eric Wedge said. "We wanted to play."
Both Wedge and Texas manager Ron Washington will keep their starting rotations intact.
Right-handers Tommy Hunter (7-3) of Texas and Carlos Carrasco (0-1) of the Indians are scheduled to start the first game. Rangers right-hander Brandon McCarthy (6-2) will face left-hander Aaron Laffey (7-4) in the second game.
"We'll keep it the same," Washington said, adding that he hopes the rain gave the Rangers' road-weary hitters enough rest to come back strong. Texas is at the end of a stretch of playing 25 of 36 games on the road and has not scored in its last 15 innings -- since the third inning on Saturday in Baltimore.
The Rangers' lineup could get a boost as outfielder Andruw Jones is due to be activated Tuesday. He has been sidelined since Aug. 25 with a strained left hamstring.
"It would be huge if Jones could step up," Washington said. "It certainly would help if he could catch fire down the stretch."
The Rangers will still be without outfielder Josh Hamilton and third baseman Michael Young. Hamilton received a second shot for a pinched nerve in his back Monday is not expected to return until at least next weekend. Young, batting .322 with 22 homers and 67 RBIs, has missed four games with a strained left hamstring.
Washington said Omar Vizquel will start at third base in the first game and Esteban German will play third in the second game. He also plans to have Ivan Rodriguez catch the first game and Taylor Teagarden catch the second game.
The rain delayed the Indians debut of catcher Lou Marson, called up from Triple-A Columbus and tabbed to catch Carrasco. Both were acquired by Cleveland from Philadelphia when 2008 Cy Young winner Cliff Lee and outfielder Ben Francisco were traded to the Phillies for four players on July 29.