Top prospect Archie Bradley was scheduled to make his first Cactus League start for the D-backs, while Edwin Jackson was set to pitch for the Cubs.
There was no immediate word on how either club will adjust its pitching rotation to get in work for the starters, as well as relievers, who were scheduled to pitch.
Arizona's afternoon game against the Brewers was called after 4 1/2 innings, following a 36-minute rain delay before the game. Chicago canceled its afternoon game against the Giants at its new spring ballpark.
Travis Wood, who was scheduled to start the afternoon game for the Cubs, threw two innings in a simulated game at the Cubs' complex to make up for the lost game.
The Cubs also will play a "B" game against the Angels on Monday to make up for the lost innings.
D-backs relievers who did not make it into the afternoon game, including Joe Thatcher, pitched to hitters in the covered batting cages.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. Chris Gabel is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.