The Journal News, citing Westchester County clerk records, said on its website that the filing occurred on May 12, three days before Kennedy's wife, Mary Richardson Kennedy, was charged with drunken driving.
It said details, including any grounds cited for divorce, were not available.
Calls to Robert Kennedy and to Mary Kennedy's attorney were not immediately returned. The Journal News quoted Kennedy as saying, "I'm not going to talk to you about my personal life."
Kennedy, a prominent environmentalist, is the son of assassinated Sen. Robert F. Kennedy and nephew of assassinated President John F. Kennedy. Mary Kennedy is his second wife. They have four children.
Kennedy had two children with his first wife, whom he divorced in 1994.
Mary Kennedy was arrested May 15 after a police officer reported seeing her drive her car over a curb near their home in Bedford, 45 miles north of New York City. Police said she had a blood-alcohol level of 0.11 percent; the legal limit is 0.08 percent.
Robert Kennedy did not appear at his wife's May 28 arraignment, when she pleaded not guilty and agreed to be evaluated to see if she needs treatment for alcohol abuse.
Police said they had responded to the Kennedy home twice in the week before her arrest but no crimes had been committed.
Lt. Jeff Dickan said that in one call, Mary Kennedy reported a dispute between children. He said the other visit resulted in a state domestic incident report but there were "no crimes committed, no report of assault, no arrests and no need for follow-up."