The blast - which took place at about 7am yesterday (8pm Singapore time) in the station at the Port Authority bus terminal, not far from New York's iconic Times Square - sparked commuter panic and travel disruptions.
President Donald Trump used the attack to call for tougher United States immigration rules, saying the current "lax" policy "allows far too many risky, inadequately vetted people to access our country". He urged New Yorkers to report any suspicious activities to the police.
Addressing the press on the matter, Mayor Bill de Blasio said the man acted alone and no other incidents have been reported.
People reported seeing the bomb squad responding and posted images of the scene on social media.
Miller cited the attacks of September 11, 2001, that killed more than 2,750 people in NY and almost 3,000 people total; and the World Trade Center bombing of February 26, 1993, which killed six people. They said the attack appears to be isolated.
The incident was captured on security video, police said.
Cuomo told cable news channel NY1 that officials "have reason to believe that this person went to the internet and found out how to make a homemade bomb".More news: Flu season could be worse this year, doctors say
"There was a stampede up the stairs to get out", said Mr Diego Fernandez, one of the commuters at Port Authority. Avoid the area. Subways bypassing #PortAuthority and Times Square Stations. "Everybody was scared and running and shouting".
Police stand guard at the Port Authority Bus Terminal.
"A woman fell, and nobody even stopped to help her because it was so insane", she said.
According to the New York Post, the suicide bomber suspect is a Bangladesh native, 27, who now lives in Brooklyn.
The suspect had attached the pipe bomb to himself with a "combination of Velcro and zip ties", according to New York Police Department commissioner James P. O'Neill. On a typical weekday, about 220,000 passengers arrive or depart on more than 7,000 buses.
President Donald Trump has been briefed on the incident, White House spokeswoman Sarah Huckabee Sanders told reporters.
The Port Authority is a transportation hub where buses and trains operate.