Three females and two males were shot in the Keyham area of the city.
Two of the females died at the scene, along with the men. The third died shortly afterward in hospital.
Luke Pollard, MP for Plymouth Sutton and Devonport wrote on Twitter that one of the victims was a child under the age of 10.
"I'm utterly devastated that one of the people killed in the Keyham shooting was a child under ten years old," he wrote.
Police have since confirmed that one of the victims was a "very young girl."
The incident, the worst mass shooting in Britain since 2010, is not terror-related, police said.
Police were called to Biddick Drive at about 6.10pm on Thursday with the South Western ambulance called a few minutes later.
Pollard said it's thought the shooting began in Biddick Drive and spread to nearby streets.
Some of those injured in the incident are still in hospital,
Sky News quoted him as saying.
"An awful lot of people who seem to be caught up in this shooting."