The 14-time French Open champion is scheduled to play in the singles and in the men's doubles alongside rising star and fellow Spaniard Carlos Alcaraz at Roland Garros.
"He had some discomfort yesterday (Wednesday) morning," Moya told Spanish radio.
"In the afternoon he was more limited and before it got worse he decided to stop."
The 38-year-old Nadal did not train on Thursday, which Moya said was "the most responsible thing to do".
"Don't force it at the moment and see if he recovers well," he added. "We will see what condition he's in tomorrow and Saturday."
Nadal returned to tennis this year after a lengthy absence with a hip injury, reaching his first ATP final since winning the 2022 French Open in Bastad last weekend before losing to Portugal's Nuno Borges.
He is scheduled to face Hungarian Marton Fucsovics in the singles first round on Sunday, the day after partnering Alcaraz in the doubles.
If Nadal defeats Fucsovics, he would set up a possible second-round meeting with old rival Novak Djokovic.
"I can't guarantee anything, neither that he won't play or he will play," said Moya. "At the moment he needs to rest, undergo treatment.
"He is obviously very excited to play these Olympics. It has been something marked on his calendar for years.
"He is a born competitor and wants to play singles and doubles. He's very excited about the doubles with Alcaraz. It will be the first time they have played together and it will be something historic for Spanish tennis."
Nadal is a two-time Olympic champion, having won singles gold in Beijing in 2008, and doubles gold at the 2016 Rio Games alongside Marc Lopez.
