"He was much better today, so we just have to wait and see how he is in another day or so," Jocketty said.
Homer Bailey has moved up a day to take the assignment of Game 3 vs. the Giants' Ryan Vogelsong. Cincinnati has not named a Game 4 starter yet.
"We're going to do what's best for [Cueto]," Reds manager Dusty Baker said. "I just hope that's good for us, too."
Cueto did not miss a start the entire season and led the Reds' pitching staff by going 19-9 with a 2.78 ERA in 33 starts and a career-best 217 innings.
The Reds are trying to avoid replacing Cueto on the roster, because the rules say that a removed player must miss the next round of the playoffs. That would mean Cueto would not be eligible until the World Series, if Cincinnati can get that far.
If Cueto was unavailable for a Game 4 on Wednesday, Game 1 savior Mat Latos could possibly return on three days of rest. Latos pitched four innings of relief in the 5-2 win over San Francisco after Cueto exited.
Leading the best-of-five series over the Giants by a 2-0 margin, the Reds have a chance to close it out with a sweep Tuesday, airing at 5:30 p.m. ET on TBS. With the NL Championship Series not set to begin until Sunday, it would give the Reds more time and Cueto more time to get treatment for his back.
"If we can win tomorrow and close it out, that'd be great, one of the next two definitely," said Game 2 winner Bronson Arroyo on Monday. "If we have to go to a Game 5, somebody is probably going to have to pitch on three days' rest, or we're going to have to take Johnny off the roster, which would eliminate him for the next round. So something probably wouldn't be in our benefit if we had to go deeper into the series.
"If we can close it out [Tuesday], it'd be great to give our bodies a little bit of a rest and give us a chance to evaluate some other guys and see what we need for Round 2."
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, and follow him on Twitter @m_sheldon. Mark Clements, an associate reporter for MLB.com, contributed. This story was not subject to the approval of Major League Baseball or its clubs.