Both teams waited nearly 90 minutes before the game was canceled at 6:38 p.m. PT.
Monday's game will be made up on Tuesday, as part of a doubleheader. The first game is scheduled for 2:10 p.m.
Right-hander Ervin Santana, who was scheduled to pitch on Tuesday, will start in the first game against Kansas City's Sidney Ponson. Right-hander Sean O'Sullivan, who was scheduled for Monday, will pitch against Bruce Chen in the second game.
The nightcap will start 30 minutes after the conclusion of the first game, unless the first game concludes before 4:40 p.m., at which point the second game will begin at its original time of 5:10 p.m.
Angels manager Mike Scioscia said he tabbed Santana to pitch the first game, because Santana will get the benefit of knowing exactly when the game will start.
"It'll be good for Ervin to pitch the first game, so he can go through his whole routine," Scioscia said.
Scioscia said he was glad Monday's game was rescheduled for Tuesday. The Angels do return to Kansas City for a four-game series in September, but the Angels are looking at a busy September schedule.
The Angels have already had two games postponed -- a game at home on April 9 against Oakland, and a game in New York on May 3.
The Oakland game was rescheduled for Aug. 27, while the New York game will be made up on Sept. 14.
"August and September for us is packed," Scioscia said. "We already have two make-up dates with Oakland and New York. I think [we should] just try to get in now."
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.