Schmidt is dealing with some shoulder soreness, manager Aaron Boone told reporters in Florida. Clarke Schmidt is going to have a bullpen session instead of facing the Blue Jays.
The 29-year-old Clarke Schmidt went 5-5 with a 2.85 ERA in 16 starts for the Yankees last season.
New York has been hit hard by injuries during spring training. Ace right-hander Gerrit Cole is out with a season-ending elbow injury.
Right-hander Luis Gil, who won the AL Rookie of the Year award in 2024, has a lat strain, and designated hitter Giancarlo Stanton is sidelined because of pain in his elbows.
New York won the AL East last year and lost to the Los Angeles Dodgers in the World Series.
The Yankees lost Juan Soto in free agency, but they added Max Fried, Devin Williams, Cody Bellinger and Paul Goldschmidt to their roster.
Clarke Schmidt has only appeared in one game so far this spring after being slowed early by a cranky back.
The Yankees had planned for him to start the sixth game of the season - with the potential for the Opening Day starter, Carlos Rodón, to pitch the fifth game on normal rest because of a pair of early off-days - so Clarke Schmidt could build up as much as possible before heading north, but now that may be in jeopardy.
Clarke Schmidt made his Grapefruit League debut on Tuesday and got tagged for three runs on four hits while striking out four across 1 2/₃ innings and 38 pitches.
Lefty Brent Headrick, who has been built up to 50 pitches to give the Yankees the option to use him as a starter or multi-inning reliever, will start in Schmidt's place on Monday.
Clarke Schmidt missed over three months last season with a lat strain.
In 2021, he missed the first four-plus months of the season with an elbow strain.