The game was finally called shortly before 11 p.m. EDT after rains left large puddles in the outfield.
The Nationals and Giants will play a doubleheader Thursday, with the first game to begin at 4:30 p.m.
Johnson, 45, was announced as the starting pitcher for San Francisco in the opening game Thursday, when he will try to become the 24th pitcher to reach 300 major league victories.
He would become the sixth left-handed pitcher to reach that milestone. It will be Johnson's first attempt to get to the 300 mark.
In addition, Johnson would become the second-oldest pitcher to reach 300 victories. Phil Niekro achieved the feat when he was 46 years, 188 days old on Oct. 6, 1985.