The 22-year-old Ross was scheduled to make his Major League debut Saturday against the Chicago Cubs.
He joins Washington after going 2-2 with a 2.81 ERA in nine starts for Harrisburg and ranks fourth in the Eastern League with 54 strikeouts. The Nationals acquired the 6-foot-4 Ross in last winter's three-team deal with the Rays and Padres.
Cole (0-0, 5.79) appeared in three games for Washington.
Washington also moved right-handed pitcher Craig Stammen to the 60-day disabled list with a strained forearm.