Lincolnshire police said they were not looking for anyone else following the "firearms incident" near a swimming pool and sports complex in the town of Spalding.
"Three people have been fatally wounded, including the suspected offender," the police force said in a statement.
"There is an ongoing police investigation and at this stage we are not looking for anyone else in connection with the incident.
"There is no indication that this is a terrorist-related incident and no shots have been fired by police."
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Police urged members of the public to stay away from the area, and local councillor Gary Taylor said the incident had left the community reeling.
"It's terrible news and local people are very shocked," he told the Press Association news agency.
"It's a very quiet place. Gun crime does not exist in this area at all. It's shocking news."
In a short statement on its Facebook page, the Castle Sports Complex and Swimming Pool said it was closed "due to an incident in the local area".