Police negotiators were locked in an armed stand-off with a man at a house in a small rural village on Tuesday evening.
Lincolnshire Police said a "significant number" of officers were at the property in Sutton St James, Fenland, including armed police and specially trained negotiators.
A force spokesman said a "sterile cordon" had been imposed in "four or five" streets close to the incident in Chapelgate, leaving residents housebound or unable to return to their homes if they were out when the siege began.
The force refused to go into detail about the situation at the house, but sources confirmed that a man armed with a gun was inside the property.
"The incident is ongoing and we are currently unable to provide further information for operational reasons," the police spokesman said.
Local people not already at home have been asked to go to nearby houses of friends or relatives while officers deal with the incident or to make their way to Sutton St James Primary School in Bells Drove.
Staff and volunteers from the British Red Cross have set up a rest centre for residents in the area affected by the road closures.
Joy Clift-Hill, British Red Cross operations director for Lincolnshire, said: "We are working closely with the police, and our highly trained British Red Cross staff and volunteers will remain at the centre for as long as we are needed."
Police have advised motorists to avoid the village altogether.
Police said rumours circulating on the internet that the injured police officer had been shot were untrue.
A woman working at the Chapelgate post office said she had heard from family members also working in the village that the policeman was seen walking into an ambulance and was not badly hurt.
She did not want to be identified but said: "I think the policeman had some kind of facial injuries.
"The village has been shut down - the police have cars at a lot of the junctions coming into the village and they won't let anybody in."
She said she had heard that a shot was fired at a passing police car in which the officer who was injured was travelling.
"I didn't see it myself," she said, "and maybe his injuries are from glass or something, but people said he wasn't badly hurt.
"They took the police car he was in away on a low loader."