Loujain al-Hathloul, 25, and Maysa al-Amoudi, 33, have been in detention for nearly a month.
The women's cases had reportedly been transferred over comments they had made on social media - rather than for their driving, according to activists.
Saudi Arabia is the world's only country to forbid women from driving.
While it is not technically illegal for women to drive, only men are awarded driving licences - and women who drive in public risk being fined and arrested by the police.
Saudi women have launched a series of campaigns - including on social media - to demand an easing of the restrictions.A Saudi activist and writer, Hala al-Dosari, told the BBC's Newshour programme that the transfer of the women's cases was being seen as "a continuation of the effort of the authorities to curb dissent".
"This is not an isolated case," she said. "This is just a way to really curb the momentum of campaigning and [the] engagement of citizens."
Ms Hathloul was arrested on 1 December after she tried to drive into the kingdom from neighbouring United Arab Emirates (UAE), according to the AFP news agency.
Ms Alamoudi, a Saudi journalist based in the UAE, was also arrested when she arrived at the border to support Ms Hathloul, the agency says.
Both women have a large following on Twitter. Ms Hathloul tweeted about her day-long wait at the Saudi border as she tried to enter the country.
On Thursday, a court in al-Ahsa, in the east of the country, ruled that the women should be tried at a specialised court in Riyadh that was established to deal with terrorism cases.
Activists say lawyers for the women plan to appeal against the transfer.
