"It's what we thought -- a deep quad contusion," said Royals manager Ned Yost.
Yost said Perez, the reigning World Series Most Valuable Player, will be out 7-10 days. In the meantime, the Royals recalled catcher Tony Cruz from Triple-A Omaha and optioned right-hander Peter Moylan there.
Cruz was hitting .278 with six doubles, three homers and 20 RBIs in 31 games for the Storm Chasers this season.
"We're hoping to get Sal back relatively soon," Yost said. "It's in the 7-10-day range. Could be sooner, could be a little longer. We have to wait and see for the blood to get out of there and get it to heal up."
The recovery time made it difficult for the Royals to put Perez on the disabled list.
"We're kind of [caught] in between, because we [would] hate to DL him and then he's ready sooner than that," Yost said. "We're better off to try to get through it with 12 pitchers and see what happens."
Perez was at the stadium on Sunday and watched the Royals' 5-4 win.
"As soon as Cheslor hit me, I thought it was going to be worse," Perez said. "But after the MRI, we're thinking a [few] days. I don't know exactly how many days, but I will do my best to get into the lineup.
"Of course, [I was scared] before the MRI, but after the MRI, [trainer Nick Kenney], the best trainer in the league, he talks to everyone like his son, he said everything is not right but it could be a lot worse."
Kenney pointed out that Perez also has a bone bruise on his knee that will take some time to heal, but that it was "playable."
Perez was injured in the ninth inning on Saturday as he pursued a foul pop about halfway between home plate and third base. Cuthbert was also in pursuit and collided hard into Perez's leg.
Perez fell to the ground and immediately signaled for the team's trainers. He needed to be helped off the field.
"When it happened, I thought he was done [for the season]," Yost said.
Cuthbert also was relieved by the positive news.
"We couldn't hear each other," Cuthbert said of the play. "I should have looked up sooner. So [I'm] glad he's OK."
Cuthbert seemed to take responsibility for the collision.
"It was going to be a more difficult play for me," Cuthbert said. "I think next time I should look where he's at. I kept running right for the ball."