Maksim Gelman, 23, was arrested at a subway station, the cable television news channel NY1 reported.
During a span of 28 hours in Brooklyn and Manhattan, Gelman allegedly fatally stabbed his stepfather, Aleksander Kuznetsov, 54; ex-girlfriend, Yelena Bulchenko; and her mother Anna, 56; and fatally struck a pedestrian, Stephen Tanenbaum, 62, while driving a car he had stolen from a man he wounded with a knife.
Police Commissioner Ray Kelly said police were trying to investigate Gelman's motive.
"He made a statement that 'she had to die,'" Kelly said. "There are two female victims here. We're not certain which one he's referring to that. But other than that, we know no specific reason why.
"Obviously, if he wasn't apprehended this morning, he could have injured, killed many more people."
He also allegedly stabbed a taxi driver and cut a couple before making a 40-year-old train passenger his final victim before being apprehended.
Two officers arrested him aboard the train after knocking a knife out of his hand.
The wounded victims were expected to survive.
NY1 said Gelman has 10 prior arrests, mostly for drugs and graffiti.