The suspects were in a "vehicle of interest" heading east at around 8.45pm Sunday night Eastern Time on the Belt Parkway from the Verrazano-Narrows Bridge, the FBI confirmed. A weapons stash was found inside the SUV, the New York Daily News reported.
A government official and a law enforcement official who were briefed on the investigation said the five people were being questioned at an FBI building in lower Manhattan.
New York State Senator Marty Golden posted on Instagram that the arrests had "a possible connection to the bombing" in Chelsea.
No one has been charged and the investigation is ongoing, the FBI said.
The bomb that tore through Chelsea contained residue of an explosive often used for target practice that can be picked up in sporting goods stores, a federal law enforcement official said on Sunday.
The discovery of Tannerite could be vital as authorities try to work out whether the bomb was linked to another device, believed to be a pressure cooker with wires coming out of it, found a few blocks away.
A pipe bomb earlier exploded in a New Jersey coastal town ahead of a charity race on Saturday morning. No Tannerite is thought to have been found at that site.
Mobile phones were discovered at the site of the blasts in Manhattan and Seaside Park, New Jersey, but authorities said they didn't appear to be connected, though they weren't ruling anything out.
An unidentified 911 caller who said he was near the scene when the blast scattered shrapnel across a street outside an Orangetheory gym in Chelsea had warned of further bombs to come.
Investigators identified a person of interest in the bombing through surveillance footage, but it is unclear if he was among the five arrested.
New York Governor Andrew Cuomo called the Chelsea explosion "an act of terrorism", but said there was "no evidence" of ties to an international group. He said the device appeared "similar in design" to the first.
Mayor Bill de Blasio said there was "more work to do" before authorities could say what the motivation was for the attack on the area known for its vibrant arts scene and large gay community.
In a bizarre twist, a blog emerged after the attack claiming credit for the bombing and saying it was a call for gay rights. The Tumblr account was taken down early Sunday afternoon and investigators said they did not believe it was relevant to the case.
The bombing is one of three "terror attacks" on US soil in one day, including a mass stabbing at a Minnesota shopping centre claimed by Islamic State and a pipe bomb explosion in New Jersey ahead of a charity race.
New York City police said they were going to blow up the second device found blocks away from the first bomb.
