The knockout tournament, the oldest ongoing football competition in North America dating back to 1914, was due to kick off on May 18 after being cancelled altogether in 2020 due to the pandemic.
However US Soccer's Open Cup committee said "logistical and financial challenges" made a May start date impractical.
"The logistical and financial burdens to have the tournament take place this spring in the current environment are substantial," said Open Cup Commissioner Paul Marstaller.
"Even though all of US Soccer's member professional teams will be playing in their respective league competitions this year, the Committee did not feel it wise to have clubs divert important resources during the next two months for Open Cup play.
"Instead, we will look further into the future to see what possibilities might exist for 2021. After that, a full-scale 2022 Open Cup is less than a year away."