The violence broke out on Sunday when unknown men attacked a prison in Qatif.
A two-year-old child and her mother were also among the wounded.
The victims were on a car passing through a security checkpoint when they were shot by security forces.
Saudi authorities have not commented on the incident.
Since February 2011, protesters have held demonstrations on an almost regular basis in Saudi Arabia, mainly in Qatif and the town of Awamiyah in Eastern Province.
The demonstrations turned into protests against the Al Saud regime after November 2011, when Saudi security forces killed five protesters and injured many others in the province.
Source: Press TV