The Okaz daily did not name the accused, but gave her age as 43.
It said she is "the first woman accused of being involved in terrorist activities" in Qatif, a coastal district where Shiites form the majority.
In 2011, Shiite protests began in the area and developed into a call for equality in the Sunni-majority Gulf country.
Most of Saudi Arabia's Shiites live in the oil-rich east, where they have long complained of marginalisation.
More than 200 men have been convicted in relation to the protests, and some were sentenced to death, said Ali Adubisi, director of the European Saudi Organisation for Human Rights in Berlin.
He identified the accused as Naimah Almatrod, a nurse, and confirmed that she is the first woman to go on trial in connection with the Qatif demonstrations.
"She is totally innocent" of anything other than protesting, he told AFP, describing her as a "human rights defender".
At a hearing in Riyadh on Monday, prosecutors accused her of offences including "destabilising security, negatively affecting the social fabric, wreaking havoc, (and) inciting sectarian sedition", Okaz said.
She is also accused of using social media to "incite against the government and justice".
The accused asked the court for more time to prepare her defence "and to appoint a lawyer", Okaz added.
Adubisi said it was unclear what sentence Almatrod could face if convicted.