The suspect, believed to be a 29-year-old Uzbek national, was shot in the stomach before being arrested.
The media named him as Sayfullo Saipov, an immigrant who came to the US in 2010.
The incident took place along the normally gridlocked West Side Highway, a major thoroughfare that runs along the western edge of Manhattan by the Hudson River. Manhattan is the most densely populated borough of the New York City.
After smashing the truck into the school bus, injuring two adults and two children, the suspect exited the truck displaying "imitation firearms" and was shot by police, according to the New York police department (NYPD).
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An official said he rented the truck from a Home Depot in New Jersey.
The victims included a Belgian citizen and five Argentinians.
The truck driver shouted 'Allahu Akbar' after getting out of the vehicle, New York Post reported.
New York City mayor Bill de Blasio said the incident was being treated as an act of terror, "a particularly cowardly act of terror".
US President Donald Trump denounced the attack, saying "we must not allow ISIS to return".
"In NYC, looks like another attack by a very sick and deranged person. Law enforcement is following this closely. NOT IN THE U.S.A.!" Trump tweeted.
"We must not allow ISIS to return, or enter, our country after defeating them in the Middle East and elsewhere. Enough!" he said in another tweet.
The US Justice Department said in a statement that a joint terrorism task force that included the FBI, the NYPD and others was investigating the attack.
Acting Secretary of Homeland Security Elaine Duke has been briefed on the apparent act of terrorism that occurred in New York City, an official statement said.
The department is closely monitoring the situation and working with federal, state and local partners in responding to and investigating this tragedy.
"We are referring all questions about the investigation to the FBI and the New York Police Department," the statement said.
The most recent violence from terrorism there came in September 2016, when a man set off shrapnel-packed explosives in the Chelsea neighbourhood of Manhattan. Nobody was killed, but 30 people were injured.
Trucks have become a common weapon for terrorists in recent years.
In July 2016, as thousands of people crammed into the streets of Nice, France, for a Bastille Day celebration, an assailant influenced by Islamic State drove a 19-ton cargo truck into a crowd, leaving 86 dead and 434 injured.
Three months later, a man drove his car into pedestrians on Londons Westminster Bridge, killing four and injuring dozens more, before jumping out and fatally stabbing a police officer and being shot dead by other officers.
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