Chukwueze, 21, has not featured for Villarreal since aggravating a groin problem in their 4-0 win at Celta Vigo in early January, the injury causing him to miss La Liga games against Tenerife, Granada, Huesca, Girona, Real Sociedad and Levante.
A source with knowledge of the situation told ESPN that the Nigerian Under-17 World Cup winner had been playing through pain for most of the season, and on Thursday the player posted a post-op pic of himself in a hospital bed.
Villareal confirmed that Chukwueze had undergone successful surgery in Germany.
"Samu Chukwueze, who has been out injured receiving treatment for discomfort in his groin, has undergone surgery this morning [Thursday] by Doctor Ulrike Muschaweck in Munich, hoping to definitively relieve him of the said pain," Villareal said in a statement posted on the official club website.
Chukwueze told ESPN he would be absent for at least a month.
"It is always difficult for me to accept to be off the field," Chukwueze told ESPN.
"But in the big picture, four to five weeks is not so bad, and I'm happy to be able to come back and play many games this season and help my team to keep winning."
Nigeria coach Gernot Rohr is expected to name his Super Eagles squad for the final AFCON qualifying games later this month, and that timeline effectively rules Chukwueze out of contention.
Chukwueze expressed his disappointment at the prospect of having to miss Nigeria's final two games of the series, away to Benin on Mar. 22 before hosting Lesotho in the final match of the campaign on Mar. 29, but he insisted that he would not rush back to action before he was 100% fit even through Nigeria must win one match to secure qualification.
"I am always positive that my body will recover quickly so that I will not miss many games for my club or the national team," he told ESPN. "So I will work hard and do everything to come back quickly, but I won't rush so much that it means risking injury again."
Chukwueze has enjoyed a fairly quiet season to date, making just six starts in 17 appearances for Villarreal -- a marked departure from last season, when he made 20 starts among 37 total appearances, missing just one game.
"The injury has been bothering me for some months and the club has been supportive to allow me to make the final decision," Chukwueze told ESPN.
"Mentally it is difficult when an injury is just there with you for so long, so finally I said I need to be playing at 100% instead of 80-90% of my best. And I thank my club for understanding."
Chukwueze has nevertheless set a Villarrael record in becoming the youngest player -- 21 years, seven months and 11 days -- to make a century of appearances for the Spanish club.
The previous mark of 21 years, seven months and 20 days was set by Mateo Musacchio.
Chukwueze said to expect the imaginative unpredictability and magic of old when he does return.
"This season has been OK so far but I just want to get back to being 100%. I am just excited to be able to show my full talent and not be thinking anymore about injury. I believe our fans can expect some highlights."
Chukwueze has scored two goals for Nigeria in AFCON qualifying, and his partnership with forward Victor Osimhen, a fellow 2015 Under-17 World Cup winner, has yielded six goals.