The emergency doctor at Qatif Central Hospital said at least 70 had been injured, “some very critically”.
Witnesses reported a huge blast at the Imam Ali mosque in the village of al-Qadeeh, in Qatif governorate.
It is the first such incident in Saudi Arabia amid rising tension in the wider region between Sunni and Shia Muslims.
The Islamic State (IS) group said it was behind a similar attack on a Shia mosque in neighbouring Yemen on Friday, which injured about a dozen people.
But it said nothing about the bombing in eastern Saudi Arabia and no other group has said it was behind the attack.
Television pictures of the Saudi bombing showed shattered glass and debris inside the mosque, where scores were said to have been praying.
Qatif hospital has issued an urgent call for blood donations and called in off-duty staff to cope with the high number of casualties.
A spokesman for the Saudi interior ministry said the bomber detonated a suicide belt inside the mosque, causing a number of people to be “martyred or wounded”.
“Security authorities will spare no effort in the pursuit of all those involved in this terrorist crime,” the official said in a statement carried by state news agency SPA.
Saudi Arabia’s large Shia Muslim minority is mainly based in the Eastern Province, and there have been sporadic protests by Shia there for greater rights.
The attack on Friday comes at a time when the Saudis are leading a coalition of Arab states in an air campaign against Shia rebels in Yemen.