The suspect, a 29-year-old man, was shot in the stomach before being arrested.
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.
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"Eight people were killed, 11 have serious but non-life- threatening injuries," the police said.
The incident that took place in Manhattan, the most densely populated of New York City's 5 boroughs, has sent shocking waves across the country.
"The President has been briefed on the incident in NYC by Chief of Staff (John) Kelly and will be continually updated as more details are known. Our thoughts and prayers are with all those affected," White House Press Secretary Sarah Sanders.
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.
"We are referring all questions about the investigation to the FBI and the New York Police Department," the statement said.
"We have recently seen attacks like this one throughout the world.DHS and its law enforcement partners remain vigilant and committed to safeguarding the American people," it said.
According to the police, at approximately 3:05 pm (local time) the suspect drove a rented Home Depot truck onto the bike and pedestrian path at West St/Houston St driving south.
While driving south on the path the truck collided with a school bus at West St & Chambers St. After colliding with the school bus, the man exited holding two firearms. An officer assigned to the area fired, striking him in the stomach, the police said.
Following a briefing from FBI officials, Senate Minority Leader Chuck Schumer as one of thousands of New Yorkers who regularly rides on the path where this attack took place, he is grateful to the NYPD and first responders who work day in and day out to keep people, and to those that responded to the scene today.
"As the investigation unfolds, it's critical that we learn what we can from this incident and do everything we can to prevent this from happening again. The scourge of terrorism is unfortunately still with us, and we must remain vigilant as ever," Schumer said.
"Tonight and in the days ahead, we join in mourning the dead, praying for the wounded, and sending our love to the people of New York City," she said.
"Aswe await further news, we must continue to be smart and strong to keep the American people safe, not reckless and rash.Our nation's courage and resilience will always defeat the hatred and violence of terrorists," Pelosi said.