Three times a World Player of the Year, the 34-year-old plays for Racing 92 in the French capital.
The AFP news agency cited a police source as saying he was found to be over the limit after a roadside test, but was not arrested or detained.
"I've let down my club, fans and most importantly my family," Carter said.
He added in a Facebook post: "I am sure a lot of you have seen the headlines. No excuses.
"I will have to now let the police/court process run its course and face the consequences. I am just glad no one was harmed. Sorry."
Carter is regarded as one of the sport's finest fly-halves and was a World Cup winner with the All Blacks in 2011 and 2015.
Former New Zealand fly-half Dan Carter has apologised for "a massive error of judgement" after reports he was stopped for drink-driving by police in Paris.