Devon and Cornwall Police said three females and three males have died. One of the men is believed to be the attacker. The “serious firearms incident” happened at around 6pm on Thursday.
Police were called to Biddick Drive in the Keyham area at around 6.10pm.
In a statement, Devon and Cornwall Police said: “Police were called to a serious firearms incident in Biddick Drive, in the Keyham area of Plymouth at around 6.10pm today (August 12).
“Officers and ambulance staff attended the scene.
“Following attendance at the scene, two females and two males were deceased at the scene.
“A further male, believed to be the offender, was also deceased at the scene.
“All are believed to have died from gunshot wounds.
“Another female treated at the scene for gunshot wounds, died a short time later in hospital.
“All of the next of kin of the deceased have been located and informed by Devon & Cornwall Police officers.
Plymouth Moor View MP Johnny Mercer earlier said the incident was “not terror-related”.
Home Secretary Priti Patel issued a statement on Twitter urging members of the public to “remain calm”.
She 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.”