The Liverpool Women's Hospital said it immediately restricted visiting access until further notice and patients had been diverted to other hospitals "where possible".
The incident occurred at 10.59am as the country was preparing to fall silent for Remembrance Sunday commemorations.
The Liverpool Women's Hospital is just a kilometre from Liverpool Cathedral where military personnel and veterans were joining civic dignitaries from across the city for a service.
Merseyside Police said: "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 force added that "this has not been declared a terrorist incident at this stage although out of caution CT detectives are leading as we try to understand the circumstances behind the explosion".
Armed police are currently at an address around 2.4km away from the scene of the explosion.
Residents in Rutland Avenue, Sefton Park, have reportedly been told to remain indoors and the long street of Victorian houses has been sealed off.
- with AP
