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.

As a result, how - and not just whether - a claimant is able to accomplish tasks like walking and planning journeys will help determine the amount they are entitled to in benefits.
Claimants who manage the tasks, but not "reliably", will get higher payments.
Ministers admitted there were concerns that the proposals were "unclear".
The Personal Independence Payment (PIP) will replace the existing Disability Living Allowance (DLA) in April. People who are less mobile will be entitled to higher payments.
Campaigners had warned that people deemed capable of walking more than 20 metres could receive lower payments - even if they were unable to do so "safely, reliably, repeatedly and in a reasonable time period".
Ministers had previously denied the claim and argued that these words did not need to be written into legally binding regulations.
But minister for disabled Esther McVey said on Thursday: "I know that disabled people and their representatives feel strongly that this important concept is set out in law and I am happy to do this."
She added: "Our intention has always been the same - we want to target support at those who need it most.
"We have always said that we will not just look at whether individuals can carry out activities but also the manner in which they do so."
Critics of the government's changes say one third of disabled people live in poverty and an estimated 42% fewer people would be eligible for mobility allowance as a result.
In exchanges in the House of Lords last week, Crossbencher Baroness Grey-Thompson, a Paralympic gold medallist, criticised the government for its "lack of consultation with disabled people" about the proposals.
Fellow crossbencher Lord Alton has said the fact people will have specially adapted vehicles taken away from them had caused "widespread disbelief and considerable distress".
For ministers, Lord Freud conceded: "I have to accept that there was inadequate discussion of the changes and that there is inadequate understanding of them."
Hundreds of people have reportedly been fleeing a town in eastern Saudi Arabia after weeks of clashes between the security forces and armed men.
[NEXT_CONCEPT]
Regulations governing eligibility for benefits for disabled people will be changed after criticism of their likely impact, the government has announced.