TAMPA -- New York Yankees right-hander Clarke Schmidt will begin the season on the injured list after being slowed by a shoulder injury this spring, general manager Brian Cashman announced Saturday, opening the door for Carlos Carrasco to make the team as a non-roster invite to spring training.

Schmidt is the third member of the Yankees' projected starting rotation that will be unavailable when the team breaks camp for opening day on Thursday, joining Gerrit Cole (elbow) and Luis Gil (lat). Cole is out for season after undergoing Tommy John surgery. Gil will miss at least the season's first two months.

On the other hand, the 29-year-old Schmidt, who had a 2.85 ERA in 16 starts last season, should not miss ample time. A minor shoulder injury surfaced earlier this month, knocking him off track to build up the necessary pitch count, but he has said he is healthy.

He's appeared in just one game this spring, throwing 38 pitches over 1 innings. He threw 32 pitches across two innings of live batting practice Thursday. The Yankees want him to be built up to 70 to 80 pitches before starting a game in the regular season.

"He just hasn't had a spring training yet," Cashman said. "He's certainly going in the right direction."

The 38-year-old right-hander, a cancer survivor, has tallied a 6.18 ERA in 41 starts over the last two seasons, but he has impressed the club in his five outings this spring, compiling a 1.69 ERA across 16 innings.

"He's had a good camp and obviously he's earned the right to come north with us," Cashman said.

Rookie Will Warren is the likely choice for the final vacant spot in the Yankees' rotation, but Cashman declined to say whether the former top prospect will be on the roster.

Warren, 25, struggled in his first taste of the majors last season, giving up 27 runs (26 earned) in 22 innings over six games (five starts). But the team has been encouraged by his performance this spring; Warren has a 4.19 ERA in 19 innings across six outings.

Cashman also announced right-handed reliever Ian Hamilton will also start the season on the injured list. Hamilton, 29, made his Grapefruit League debut Thursday, giving up a run on three hits in one inning, after being sidelined with an infection.