A taxi carrying one passenger pulled up just before 11:00 GMT – as a national two minutes’ silence for Remembrance Sunday was due to begin – and exploded.
The passenger was declared dead at the scene and is yet to be formally identified.
The male driver was injured and is in hospital in a stable condition.
Detectives from Counter Terrorism Police North West said three men – aged 29, 26 and 21 – were detained in the Kensington area of the city.
They said they were continuing to keep an open mind about the cause of the blast and were working with Merseyside Police as the investigation continued “at pace”. The security service, MI5, is also assisting.
Armed officers have carried out raids on properties in Rutland Avenue near Sefton Park, and Boaler Street in Kensington.
Specialist officers remain outside the property in Rutland Avenue, in an operation police say is linked to the explosion.
Police negotiators are on the scene, a fire crew is on standby, and a number of residents have been evacuated.
A large cordon, guarded by uniformed officers, is in place with six marked police vans and four cars stationed at the ends.
Prime Minister Boris Johnson said on Twitter: “My thoughts are with all those affected by the awful incident in Liverpool today.
“I want to thank the emergency services for their quick response and professionalism, and the police for their ongoing work on the investigation.”
Home Secretary Priti Patel also tweeted she was “being kept regularly updated on the awful incident”.
Chief Constable Serena Kennedy, of Merseyside Police, sought to reassure the public, saying events of this nature were very rare and that there would be an increased and visible police presence on the streets in the coming days.
A bomb disposal unit and fire engines attended the scene earlier, which remains cordoned off. Road closures are also in place. (Courtesy BBC)