The three men were on a "list of 23 fugitives wanted for crimes" in Qatif, the ministry said in a statement carried by the official SPA news agency.
The statement also warned that people who "harbour or conceal" any suspects "could face consequences".
Qatif is home to a significant number of the Gulf kingdom's minority Shiites, who are estimated at around 10 percent of the population and who have long complained of marginalisation by the Sunni authorities.
Six officers were wounded yesterday when their patrol came under attack in the Al-Masoura neighbourhood of Qatif.
Last month, police shot three men wanted over what authorities said were "terrorist" attacks in Qatif.
Authorities have blamed the violence on "terrorists" and drug traffickers.
Four men were executed on July 11 after being convicted of "terrorist crimes", including attacks on police and riots in Qatif.
Amnesty International has warned that 14 other Saudis face imminent execution after a "grossly unfair mass trial" in which they were convicted of rioting, theft and rebellion in areas including Qatif.
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