Merseyside Police were called to reports of a blast involving a vehicle – believed to be a taxi – at Liverpool Women’s Hospital at 10.59am on Sunday.
Counter Terrorism Police North West said three men – aged 29, 26, and 21 – were detained in the Kensington area of the city and arrested under the Terrorism Act in connection with the incident.
The male passenger of the car was declared dead at the scene and is yet to be formally identified.
The driver, also a man, was injured at the scene and remains in hospital in a stable condition.
Counter-terrorism police said they continue to keep an open mind about the cause of the explosion and are working closely with Merseyside Police.
Prime Minister Boris Johnson tweeted: “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.”
Earlier, a spokesman for Merseyside Police said: “So far we understand that the car involved was a taxi which pulled up at the hospital shortly before the explosion occurred.
“We are keeping an open mind as to what caused the explosion, but given how it has happened – out of caution – counter terrorism police are leading the investigation supported by Merseyside Police.”
The three arrests took place in Sutcliffe Street in the Kensington area of the city.
A number of locals said armed officers swooped on a terraced house in the afternoon.
Sections of Sutcliffe Street and Boaler Street remained cordoned off, with a heavy police presence at the scene as inquiries continue.
A similar police scene was in place at Rutland Avenue in Sefton Park, with counter-terror officers sighted in the neighbourhood.
Locals said police arrived from about 1pm as officers went on to guard a terraced property as the immediate surrounding area was cordoned off.
The Chief Constable of Merseyside Police, Serena Kennedy, later offered her reassurance over the incident.
She said: “While I understand that today’s incident may cause concern in our communities, it should be pointed out that events of this nature are very rare.
“Merseyside Police will continue to liaise with community groups, community leaders, partner agencies and individuals in the coming days and weeks to make sure any concerns are addressed and ensuring that we provide the best possible service to local people.
“There will also be an increased and visible police presence on the streets of Merseyside and I would encourage people to engage with my officers and raise any concerns they may have.
Ms Kennedy urged people not to speculate about what had happened.
Images of a vehicle on fire, and later burnt out, outside the hospital earlier were shared online.
Liverpool Women’s Hospital said visiting access had been restricted “until further notice” and patients had been diverted to other hospitals “where possible”.
In a statement, the hospital said: “We are reviewing our patient activity for the next 24-48 hours and patients should wait to be contacted for updates about any planned appointments or other attendance at the hospital.
“Our staff are being permitted to leave and enter the hospital under the supervision of Merseyside Police.
“We would like to say thank you for the co-operation and support of our patients, visitors and staff who have been impacted by this incident, in particular those members of staff who were at the scene at the time of the incident.”
Phil Garrigan, chief fire officer of Merseyside Fire and Rescue Service, said the car fire at Liverpool Women’s Hospital was “fully developed” when two appliances arrived shortly after 11am.
He told reporters at the scene: “The operational crews extinguished the fire rapidly but as has been reiterated by the police chief constable, there was one fatality.
“Another individual had left the vehicle prior to the fire developing to the extent that it did.
“Our thoughts are with them and the families of those involved.”
Home Secretary Priti Patel tweeted: “I am being kept regularly updated on the awful incident at Liverpool Women’s Hospital.
“Our police and emergency services are working hard to establish what happened and it is right they are given the time and space to do so.”