The authorities have been trying since May to demolish the old quarter of Awamiya, saying Shia militants use its narrow streets as a hideout.
Activists accuse security forces of trying to force out residents.
It is the latest intensification of sporadic unrest in the Eastern Province, which is largely Shia.
At least seven people, including two police officers, have been killed in the clashes, Reuters news agency said.
Local activists say Saudi forces have been firing randomly towards homes and cars, and that buildings have been damaged or burned in the fighting.
"No one is going out. If you go out, you will be shot by snipers," one activist told the BBC. People in the town were running out of drinking water, he added.
Some residents have appealed to the Saudi authorities to help them leave and families have been given accommodation in a nearby town, Saudi media reported.
Shia residents of the region around the city of Qatif have long complained that they are marginalised and discriminated against by the Sunni monarchy.
In May the UN criticised the Saudi attempt to demolish Awamiya's 400-year-old al-Masora quarter, home to between 2,000 and 3,000 people, saying it threatened historical and cultural heritage.
The Saudi authorities had imposed power cuts on residents to try to make them leave, said the UN Special Rapporteur on housing, Leilani Farha.
Anti-government demonstrations in Eastern Province began after the 2011 Arab Spring uprisings, and protests and attacks have become more frequent since the January 2016 execution of the prominent Shia cleric Nimr al-Nimr.
Sheikh Nimr, a strong supporter of the anti-government protests, lived in Awamiya.
In July, Saudi Arabia executed four people accused of carrying out terrorist acts in the Qatif region.
In the same month, two members of the Saudi security forces were killed in separate bombings in Awamiya. In June, another officer and two other people died in bombings.
During the protests, activists have accused security forces of opening fire on demonstrators, and say others are being jailed or sentenced to death for protest-related crimes.
Hundreds of people have reportedly been fleeing a town in eastern Saudi Arabia after weeks of clashes between the security forces and armed men.