Nova left Saturday night's game against Tampa Bay in the fifth inning. An MRI after the game revealed the injury and he was placed on the 15-day disabled list.
''It's hard,'' Nova said. ''I really don't know what to say. I'm sad right now.''
Nova will be further examined Monday in New York by Yankees team physician Dr. Chris Ahmad. He had no discomfort in the elbow until his 82nd and final pitch Saturday when he felt a pop.
If Nova needs elbow-ligament replacement surgery he could be sidelined more than a year.
''Usually when you have that (tear), it eventually leads to that,'' Yankees manager Joe Girardi said.
David Phelps, Adam Warren and Vidal Nuno, started and threw five shutout innings Sunday against Tampa Bay, are in the mix to replace Nova. Alfredo Aceves is starting in the minors for the Yankees at Triple-A Scranton/Wilkes-Barre.
The Yankees also, as expected, reinstated first baseman Mark Teixeira from the 15-day disabled list and he was in the starting lineup for Sunday's game against Tampa Bay.
Teixeira hurt an adductor muscle that runs alongside the hamstring trying to make a play on a foul grounder during an April 4 game against Toronto.
New York recalled right-hander Preston Claiborne from Triple-A Scranton/Wilkes-Barre and right-hander Bryan Mitchell from Double-A Trenton. Infielder Scott Sizemore was optioned to Scranton/Wilkes-Barre, while reliever Matt Daley was designated for assignment.
Closer David Robertson, on the DL with a groin strain, is expected to rejoin the team Tuesday.
Robertson felt discomfort April 6 in the ninth inning of a 6-4 win over Toronto and was placed on the disabled list. He is replacing major league saves leader Mariano Rivera, who retired after last season.