Cueto said his neck is sore and has been bothering him since his last start, John Fay of the Cincinnati Enqurier writes.
Cueto told Fay he may still start tomorrow. Wood is on his normal rest because of last Thursday's off-day.
"We knew yesterday," Reds manager Dusty Baker told Fay. "He felt better yesterday. But what happens if he goes out there and starts feeling it again in the second or third inning? Then my bullpen is all torn up.
"What made it an easy decision is this is Woody's normal day. Had it not been his normal day, then we would have had a different decision to make. As it is, Johnny will go tomorrow. There's not much difference from today to tomorrow. But, in terms of health, a lot of times that 24-hour period of hands on and loving care has a lot to do with it."
Cueto is quietly having a very good season for the Reds. After starting the season on the disabled list and missing the first month with irritation in his right biceps and triceps, he has gone 4-2 with a 1.68 ERA in eight starts to go along with a 1.006 WHIP.
Wood has suffered a bit of a sophomore slump, going 5-4 with a 5.11 ERA. He has pitched well in his last two starts, combining to go 14 innings and allowing three earned runs in a no-decision against the Giants and a victory over the Dodgers.For more baseball news, rumors and analysis, follow @cbssportsmlb on Twitter or subscribe to the RSS feed.