RIYADH: Unknown gunmen opened fire at a prison and police targets in Saudi Arabia's Shiite-populated Eastern Province, wounding a woman and her child, police and rights activists said on Sunday.

The gunmen carried out three separate shootings in two Shiite towns on Saturday, provincial police spokesman Ziad al-Rukaiti said.

"The prison in Qatif came under fire from an unknown source," said Rukaiti, referring to the prison in the Shiite town of Awamiya in the Qatif district.

Rukaiti said the shots directed at the prison were "followed by shooting at a police checkpoint" in Awamiya, and another shooting targeting a police patrol in a separate Shiite town.

Rights activists confirmed that an 18-year-old woman and her two-year-old child "were wounded by random gunfire in Awamiya."

Since early 2011, mainly Shiite towns in Eastern Province have seen sporadic protests and confrontations between police and Shiite residents who complain of marginalisation.

There are an estimated two million Shiites in the Sunni-dominated kingdom of around 27.5 million people.

The unrest first erupted after violence between Shiite pilgrims and religious police in the Muslim holy city of Medina in February 2011.

The protests escalated when Saudi Arabia led a force of Gulf troops into neighbouring Bahrain the following month to help crush Shiite-led pro-democracy demonstrations in the tiny Sunni-ruled Gulf kingdom.

Saudi King Abdullah on January 14 appointed Prince Saud bin Nayef as the new governor of Eastern Province, replacing Prince Mohammed bin Fahd who was in office since 1985 but was strongly criticised by Shiite activists for his aggressive policy towards them.

Prince Saud's appointment was welcomed by Shiite dignitaries in Eastern Province.