Witnesses described hearing gunshots on Thursday evening, with one saying she saw a man “randomly” start shooting at people in the Keyham area of the city.
Emergency services were called to Biddick Drive shortly after 6pm on Thursday.
Devon and Cornwall Police said there had been a “number of fatalities” with several other casualties receiving treatment.
The force said a critical incident had been declared, the area cordoned off, and it believes the situation is “contained”.
Local MP Johnny Mercer tweeted that the incident is “not terror related”.
One witness, who lives near Biddick Drive and gave her name as Sharron, told the BBC: “Firstly, there was shouting, followed by gunshots – three, possibly four to begin with.
“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.”
Robert Pinkerton told the BBC he had “walked around the corner” and “bumped into a bloke with a shotgun”.
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… Officers and ambulance staff attended.
“There have been a number of fatalities at the scene and several other casualties are receiving treatment.
“A critical incident has been declared.
“The area has been cordoned off and police believe the situation is contained. Road closures are in place so please avoid the area.
“We are appealing to the public not to speculate or share pictures of the scene on social media or anywhere else.”
Mr Mercer, MP for Plymouth Moor View, tweeted: “The incident is not terror related, and neither is the suspect on the run in Plymouth.
“Remain calm. It is for the police to confirm further details. Do not repost chatter or gossip; work with them. We have the best cops in the land.”
In an earlier tweet, Mr Mercer said he was “aware of a serious and tragic incident unfolding in Plymouth”.
He added: “Please obey all instructions from the police and do not post rumour or speculation on social media.”
The South Western Ambulance Service said it was called at just after 6pm on Thursday to Keyham.
The ambulance service tweeted: “We responded to the incident with a significant number of resources, including Hazardous Area Response Teams (HART), multiple ambulances, air ambulances, multiple doctors and senior paramedics.
“We will provide an update here in due course.”
Luke Pollard, MP for Plymouth Sutton and Devonport, said the situation looked like “a very grim day for our city and our community”.
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.”