Nova recently told reporters that he sprained the finger while fielding a grounder last month but that the injury did not cause him significant pain until Thursday's game against the Cincinnati Reds.
The Pirates announced the roster move before Monday's game against the Chicago Cubs. Right-hander Nick Kingham was recalled from Triple-A Indianapolis and will start in Nova's rotation spot Tuesday against Chicago.
Kontos, 32, had been designated for assignment on Friday. Kontos was removed from his role as the primary setup man for closer Felipe Vazquez last week. In 21 games, Kontos was 2-3 with one save and a 5.03 ERA.
Nova, 31, has gotten off to a rough start this season, going 2-5 with a 4.96 ERA in 11 outings. Kingham has pitched well in his three starts with Pittsburgh, going 2-1 with a 3.44 ERA.
The Associated Press contributed to this report.