The New York Post said the unidentified man, who appeared to be in his 50s, was taken to St. Luke's Hospital in Manhattan for treatment.
The newspaper did not say what type of injuries he sustained in the suicide attempt.
"There was an incident out on the plaza," "Today" co-host Matt Lauer told viewers when the show began. "A man tried to harm himself with a knife. He did manage to cut himself. He was controlled by our security team out there. ... He's being treated by medical personnel."