Anderson, a Grand Slam runner-up in each of the past two years, was set to begin his hardcourt run-up to the US Open after a third-round exit at Wimbledon.
The 33-year-old from Johannesburg, now a Florida resident, had been nursing a right elbow injury for much of the season.
Anderson, who had a first-round bye, was replaced in the draw at the US capital by Slovakian lucky loser Norbert Gombos.
Anderson was the 2017 Washington runner-up to Germany's Alexander Zverev on his way to his first Grand Slam singles final at the 2017 US Open, where he lost to Spain's Rafael Nadal.
He also reached the 2018 Wimbledon final, where he was defeated by Serbia's Novak Djokovic.
In January, 6-foot-8 (2.03m) Anderson won his sixth career ATP title at Pune, defeating 6-foot-11 (2.11m) Ivo Karlovic in three tie-breaker sets in the tallest final of the Open Era.