"He's not real happy," Girardi said. "I told him missing one game is better than missing four to six weeks, if something were to happen."
Jeter is available in an emergency Sunday against the Boston Red Sox, Girardi said. There are no tests scheduled.
Girardi said he plans to play Jeter on Tuesday at home against the Chicago Cubs. Jeter was not immediately available for comment.
Jeter plans on retiring at the end of the season. He only played in 17 games in 2013 because of a variety of injuries related to the ankle he broke during the 2012 ALCS.
Girardi said on Saturday he will not manage Jeter as if he is on a "farewell tour," but rather what is best for his team's captain and the club overall.
"He's 39 years old," Girardi said. "I think you have to be smart about it. There are times where you are going to have to give him a day off."
Sunday will be Jeter's third day off in 13 games. Prior to missing Saturday's game, Jeter had played seven games in a row. He is hitting .286 in 35 at-bats.
"I've been pleased with the way he has swung the bat," Girardi said.
Girardi said that on Friday Jeter admitted his quad tightened up after Yankees personnel noticed him doing extra stretching. It did not force Jeter out of the game on Friday. With a day game after a night game on Saturday, Jeter had a scheduled day off.
Girardi then decided that it might be better to take advantage of Monday's off day and give Jeter a total of three days off.
"Originally, my plan was to put him in there [on Sunday]," said Girardi, who changed his mind as he thought about it during Saturday's game.
Girardi thought the injury was to Jeter's right quad, but was not completely sure. Jeter has always disagreed with days off, dating back to the mid-1990s when Joe Torre was the manager.
"He's been that way since Day 1," Girardi said. "He used to fight Joe, 'How am I going to break Cal [Ripken Jr.'s] record if you keep doing this to me?' It is never a real comfortable situation when you tell him you are going to give him a day. I think he understands what I'm trying to do. His heart he just wants to be out there."
Dean Anna started at shortstop in place of Jeter on Sunday.