Turki Ahmed was arrested on orders of Interior Minister Prince Mohammed bin Nayef bin Abdel Aziz, who was tipped off by a religious organisation, they said.
The interior ministry did not confirm the arrest, however, and its spokesman was unreachable for comment.
Ahmed on his Twitter account attacked radical Islamists he said were twisting the Prophet Mohammed's "message of love," and what he described as "a neo-Nazism which is on the rise in the Arab world -- Islamic extremism".
His comments provoked fierce debate on social networking sites in Saudi Arabia between his supporters and detractors.
Online activist Raif Badawi, another Saudi, was arrested in June in Jeddah and accused of apostasy, which carries the death penalty in the Gulf kingdom.
Badawi helped set up a liberal Saudi website, which declared a "day of liberalism" on May 7, calling for protests against the stranglehold of religious officials on public life in the strict Sunni-ruled monarchy.
Amnesty International condemned Badawi's prosecution.
"Raif Badawi’s trial for ‘apostasy’ is a clear case of intimidation against him and others who seek to engage in open debates about the issues that Saudi Arabians face in their daily lives," said Philip Luther, director of the organisation's Middle East and North Africa division.
"He is a prisoner of conscience who must be released immediately and unconditionally," he added.