Merseyside Police said in a statement that they understood that the car involved was a taxi which had pulled up at the hospital shortly before the explosion occurred.
Chief Constable Serena Kennedy said police were called to reports of a car explosion just before 1100 GMT on Sunday.
“Work is still ongoing to establish what has happened,” she told media.
“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 police said the explosion had not been declared a terrorist incident at this stage.