Thunderstorms moved into the area about 6 p.m. local time and the high winds that accompanied them caused a delay in covering the infield.
With additional rain on the way and with the infield having become a sea of mud, the game was postponed.
The teams had been scheduled to play a two-game series after meeting in a double header Monday in Phoenix.
Because Arizona has a day game scheduled in Chicago against the Cubs Friday, no attempt will be made to play a double header against the Rangers Thursday. A single game will be played Thursday and the postponed game will be made up at a yet-to-be-determined date.