Vargas, who has been diagnosed with a non-displaced fracture of the hamate bone in his right hand, will undergo the operation Tuesday.
The Mets announced Monday that Vargas would return to his throwing program approximately five days after the surgery, which would give him just over a week to be ready for his scheduled turn in New York's regular-season starting rotation.
But after throwing a modified bullpen session Monday, Vargas acknowledged that he could potentially miss a start or two in April, saying his right hand needs to heal to the point where he can catch the ball and grip a bat.
"It's all going to depend on how things go post-op," Vargas told reporters, according to the New York Daily News. "But the word is that I should be able to get back to throwing in about five days after surgery -- that's definitely a positive that I won't have to be shut down and rebuild the throwing program."
Vargas suffered the injury Saturday when he attempted to catch a line drive in a minor league game.
The Mets open the regular season on March 29 at home against the Cardinals. Noah Syndergaard is slated to start the opener, and Jacob deGrom is scheduled to start the Mets' second game on March 31. Mets manager Mickey Callaway has not named a rotation beyond those first two starts.
Vargas, 35, signed a two-year, $16 million deal with the Mets last month after going 18-11 for the Royals last season. He is expected to be part of a talented Mets rotation that includes Syndergaard, deGrom and Matt Harvey.