Exactly how Freddy Garcia sliced his right index finger, he wouldn’t say. Either way, the kitchen accident that caused a small cut next to his nail needs time to heal before he can pitch again for the Yankees.

“A couple of days, probably,” Garcia said.

Sunday’s game between the Yankees and Tampa Bay Rays was rained out and no makeup date was set. It will be rescheduled as part of a doubleheader when Tampa Bay returns to Yankee Stadium on Sept. 20-22 – that last game already is a makeup from a rainout July 8.

Garcia was originally set to start Sunday. On Saturday, however, the Yankees said Garcia’s next outing was being pushed back because of the household mishap earlier in the week.

Garcia said it occurred “like five days ago.” He’d felt fine in a bullpen session since then, but later had problems with his grip for the split-fingered fastball.

“I cannot go out there and not throw my best pitch,” he said.

Yankees manager Joe Girardi said he didn’t think Garcia, 10-7 with a 3.16 ERA, would need to go on the disabled list. Girardi said he hoped Garcia would be able to start in Minnesota by the end of next weekend.

“I don’t think it’s that serious,” Girardi said.

The Yankees pushed back their rotation by a day because of the rainout. A.J. Burnett, winless in his last seven starts, was set to start Monday night in Kansas City. Rookie Ivan Nova will go Tuesday night, followed by Bartolo Colon.

This washout makes a hectic last week-and-a-half of the season for the Yankees even more scrambled, provided their playoff race with Boston and Tampa Bay isn’t decided by then. The newly created doubleheader will mean the Yankees plays 10 games in the final nine days, with all of those games against the Rays and Red Sox.

The Yankees have won 11 of their last 15. They anticipate star slugger Alex Rodriguez, out since having surgery on his right knee in mid-July, rejoining them in Minnesota.

“This club has persevered,” Girardi said. “We’ve talked about guys stepping up.”

Tampa Bay rejigged its rotation going into a day-night doubleheader Tuesday at Boston. The Rays will skip Wade Davis, who was scheduled to start the opener.

James Shields will pitch the afternoon game and Jeff Niemann will start the night game. David Price will work Wednesday.

“We don’t want to skip Price or Shields,” Rays manager Joe Maddon said.

Maddon is no fan of day-night doubleheaders. He also said the two straight days off weren’t overly welcome.

“I don’t need a doubleheader,” he said. “You don’t need all that extra time now.”