The A's said Tuesday night's game would be made up in a day-night doubleheader Wednesday. The first game is scheduled to start at 12:35 p.m. PDT and the second game at 6 p.m. PDT.
It was the first rainout in Oakland since May 5, 1998.
Cleveland beat the A's 2-0 in Monday night's season opener, which was played between rain storms that have hit the San Francisco Bay Area this week. The Indians have Thursday off before hosting Minnesota in its home opener Friday in Cleveland.
The A's open a four-game series against Seattle on Thursday in Oakland.