It said one person was crucified after his execution, a punishment reserved for particularly serious crimes.
At least 100 people have been executed in Saudi Arabia since the start of the year, according to data released by SPA.
On Sunday, four men were killed in an attack on a security services base north of the capital Riyadh in an assault claimed by the jihadist Islamic State group.
Saudi authorities arrested 13 "terrorist" suspects the next day, but they did not say where the arrests took place or if they were linked to Sunday's attack.
The interior ministry said some of those executed Tuesday were accused of "inciting sectarian strife", a charge often used in Saudi Arabia against Shiite activists.
The Eastern Province has seen bouts of unrest since 2011 when protesters emboldened by the Arab Spring took to the streets demanding an end to alleged discrimination by the Sunni-dominated government.
Although no official figures exist, Shiites make up an estimated 10-15 per cent of the ultra-conservative kingdom's 32 million population.
In January 2016, Saudi Arabia enraged Shiite Iran with the execution of prominent Shiite cleric Nimr al-Nimr, among a group of 47 people convicted of "terrorism".
Saudi diplomatic missions in Iran were attacked in violent demonstrations, prompting Riyadh to sever relations with Tehran.
Riyadh accuses Tehran of attempting to "destabilise" the region and of interfering in other countries' internal affairs.
Rights experts have repeatedly raised concerns about the fairness of trials in Saudi Arabia, governed under a strict form of Islamic law.
Executions in the ultra-conservative kingdom are usually carried out by beheading.
Last year, the oil-rich Gulf state carried out 149 death sentences, according to Amnesty International, which said only Iran was known to have executed more people.
People convicted of terrorism, homicide, rape, armed robbery and drug trafficking face the death penalty, which the Saudi government says serves as a deterrent against serious crime.
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