Melissa Schuman, then aged 18 and a Dream member, has alleged that Carter, then 22, assaulted her at his apartment while they were working on a movie, reports theguardian.com.
She said despite her telling him that "she was a virgin and didn't want to have sex before marriage", Carter forced her to have sex with him "against my will".
Carter, now 37, has denied the allegations.
"I am shocked and saddened by Schuman's accusations. Melissa never expressed to me while we were together or at any time since that anything we did was not consensual...
"This is the first that I am hearing about these accusations, nearly two decades later. It is contrary to my nature and everything I hold dear to intentionally cause someone discomfort or harm," he said in a statement.
Schuman, who later performed alongside Carter on a duet, describes being "traumatised" after the attack, saying she initially "wanted to lock it in a box in my mind and let the memories slowly suffocate as time went on".
She says she feels "an obligation now to come forward with the hope and intention to inspire and encourage other victims to tell their story. We are stronger in numbers".
Her allegations come following many accusations of sexual abuse in the entertainment industry.
In October, an unnamed woman accused Carter and a friend of sexually assaulting her in 2006.
Carter's representative said the woman "fabricated the claims against Nick for one simple reason - she was hoping to extort money from him".
Schuman says that the "victim shaming" she saw in the comments of an article about those accusations prompted her to share her story.