Devon and Cornwall Police said three females, two males and the suspect had died in the Keyham area of the city on Thursday evening.
All are thought to have died from gunshot wounds but the shooting is not terror-related, the force confirmed.
An MP said one of those killed was a child under 10 years old and more people were being treated in hospital.
Plymouth Sutton & Devonport MP Luke Pollard said the incident was "unspeakably awful" and that he was "utterly devastated" to learn one of those killed was a child.
In a statement, Devon and Cornwall Police said two females and the three males died at the scene, while one female died shortly after in hospital.
The force added: "The area has been cordoned off and police are not looking for anyone else in connection with the incident."
Eyewitness Sharron, who lives near Biddick Drive and did not want to give her full name, said what happened was "horrendous and so sad".
"Firstly, there was shouting, followed by gunshots - three possibly four to begin with," she said.
"This was when the shooter kicked in the door of a house and randomly started shooting. He ran from the house shooting as he ran and proceeded to shoot at a few people in the linear park up from the drive."
She said the "shooter proceeded along Royal Navy Avenue still shooting".
Another witness, Robert Pinkerton, said he "walked around the corner" and "bumped into a bloke with a shotgun". He said the man was dressed all in black.
People were asked to stay inside and follow police advice as the emergency services responded.
Plymouth Moor View MP Johnny Mercer earlier said the incident was "not terror-related".
Scenes of crime officers in white suits could be seen using cameras in the street and members of the public who lived locally were not allowed into their homes, PA Media reported.
Officers appealed to the public not to speculate or share pictures of the scene on social media or anywhere else.
Home Secretary Priti Patel tweeted: "The incident in Plymouth is shocking and my thoughts are with those affected.
"I have spoken to the chief constable and offered my full support.
"I urge everyone to remain calm, follow police advice and allow our emergency services to get on with their jobs."
Labour leader Sir Keir Starmer tweeted: "There's much we don't know about the shocking events in Plymouth. However it's clear tragedy has hit Keyham.
"My thoughts are with the families and neighbours of those caught up in this nightmare. I pay tribute to our emergency services who ran towards events we'd all run from."
Mr Pollard added Ford Primary School and St Mark's Church on Cambridge Road would be open from 09:00 on Friday as a "safe place for our community to come together".
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