"Hopefully maybe three, maybe four starts," Reds manager Dusty Baker said. "Once he does come back, he still has to get his endurance up. We're not putting a timetable on it. We're going to miss him. We'll find a way to carry on."
In three starts this season, Cueto has gone 1-0 with a 2.60 ERA, having tallied 18 strikeouts in 17 1/3 innings. He finished fourth in balloting for the National League Cy Young Award last season, when he compiled a 19-9 record and a 2.78 ERA.
Cueto, 27, was pitching on Saturday vs. the Pirates when he felt pain near his right triceps in the fifth inning and exited.
"This is unbelievable," Cueto said via a translator. "I felt so good. I've been pitching so relaxed that I didn't believe this could happen now the way I was feeling. One pitch I threw, I felt this and that was it."
And just like that, Cueto became the third Reds player to go on the DL in the first month of the season. He joined left fielder Ryan Ludwick (torn right labrum), who was moved to the 60-day DL to make room for Freeman, and lefty reliever Sean Marshall (shoulder tendinitis).
Cueto's injury comes with the Reds having lost five in a row during a 1-5 road trip at St. Louis and Pittsburgh.
"It stinks. There's nothing more you can say about it," Reds third baseman Todd Frazier said. "We pray that's the only thing that really happens. It's early. You want to get off to a good start, which we did. And some things happened, some struggles here and there."
This isn't the first time that Cueto has suffered a strained right lat muscle. The same injury forced him to miss the final four starts of the 2011 season.
"I don't feel this will affect me at all," Cueto said. "God willing, I will be better in about 5-6 days and able to start throwing."
That may be optimistic. Phillies ace Roy Halladay had the same injury last season and was out from May 27-July 17.
"Whenever he's out there, we always have a chance to win," Frazier said of Cueto. "Hopefully he will come back as quickly as possible. I've heard it's not as bad of an injury. We'll be fine. We've got some good guys that can be called up and do their thing."
When Cueto's turn in the rotation comes up on Thursday vs. the Marlins, it's seems likely that left-hander Tony Cingrani will be recalled from Louisville. Cingrani's start on Sunday was limited to two innings and 45 pitches, just in case he would be needed.
In his three starts this season, Cingrani has pitched 14 1/3 scoreless innings.
"Cingrani couldn't help us now, if he's going to start in Johnny's place," Baker said. "The way our bullpen is, it's taxed. We need somebody that can help us the next three days."
That person is the 26-year-old Freeman, who is getting his first big league promotion. He had a 1.80 ERA in four appearances for Louisville. After a shoulder injury early in Spring Training kept him out for an extended period, he returned to make two big league appearances at the end of camp and worked three scoreless innings.
"He's the guy throwing the best. He has good stuff," Baker said.
Jose Arredondo, who was sent outright to Louisville at the end of camp, has considerable big league experience with the Reds but was not considered. Arredondo pitched two innings on Sunday.
"[Arredondo] couldn't help us for a couple of days. We need help now," Baker said.