Two Saudi police officers were wounded during a shoot-out as they tried to apprehend one of the suspects at a house near the Kuwait border, a statement by the official Saudi state news agency, SPA, said on Tuesday.
The agency quoted a security spokesman from the Saudi interior ministry, who said the three were "parties to the crime of the sinful terrorist bombing that targeted the Imam al-Sadeq (AS) mosque in Kuwait".
One of the brothers was arrested in the western city of Taif, and another was arrested in Kuwait and later extradited to Saudi Arabia.
A fourth brother is a member of the Islamic State in Iraq and the Levant (ISIL) group and currently lives in Syria, the spokesman added.
The June 26 bombing, which occurred during the Muslim holy month of Ramadan, killed 27 people and wounded hundreds of others.
A Kuwaiti newspaper reported on Monday that 26 people had been arrested in relation to the attack in the country, according to the Reuters news agency.
The suspects included four women, and some had relatives who are members of ISIL living in the territory it holds across Syria and Iraq.
ISIL has previously claimed two suicide bombings carried out in May on Shiite mosques in eastern Saudi Arabia, where the bulk of the country's Shiite minority lives.