Authorities captured the 39-year-old suspect, identified as Benny Geritano, after he went to the hospital to get treated for lacerations on his hands caused by the attack on a busy commercial block, said Paul Browne, a spokesman for the New York Police Department.
It was not immediately clear whether the suspect had an attorney. A phone number listed for him did not ring through.
The pizzeria owner, Mark Iacono, was hospitalized in critical but stable condition with stab wounds to the face, head and back. The 43-year-old victim operates pizzeria Lucali, which GQ magazine ranked the second-best in the country in 2009.
The stabbing stemmed from an argument between the two men inside an Italian deli a few blocks from Iacono's eatery, Browne said. The dispute spilled out onto the street, where the suspect stabbed the victim with a kitchen knife.
The suspect spotted a woman he knows driving by and hopped into her car to flee to the hospital, Browne said.
He said the suspect has 10 previous arrests. In the early 1990s, he was charged twice with attempted murder but pleaded guilty to lesser charges, Browne said.
Police were investigating whether Geritano had ties to the Genovese organized crime family and whether he was trying to shake down Iacono to get a slice of his pizza empire, said a law enforcement official who spoke on condition of anonymity to The Associated Press because that part of the investigation was ongoing.
Iacono was a marble mason before he became a pizza entrepreneur in 2006 after taking over the building that once housed his favorite childhood candy store. The cozy neighborhood pizzeria he opened serves up brick-oven pizzas.
The pizzeria quickly developed a following comparable to other famous city pie parlors - with Jay-Z and Beyonce said to make regular stops at the restaurant.
A sister restaurant run by Iacono's brother, called Guiseppina's, opened last year.
A waiter who answered the phone at the sister restaurant said he had gotten a call from his boss saying they were closing early for the night because there was a "family issue." The waiter didn't give his name.
Associated Press writer Cristian Salazar contributed to this report.