The man has been identified as Ahmad Khan Rahami, 28, a naturalised US citizen from Afghanistan.
The New York Police Department (NYPD) has released a photograph.
The explosion injured 29 people.
Both the detonated bomb, and a device found nearby, were shrapnel-filled pressure cookers, according to US media.
Authorities have warned the suspect, whose last known address was in New Jersey, should be considered “armed and dangerous”.