The Operations Cell of Libyan Revolutionaries, which in principle reports to the defense and interior ministries, said on Facebook it had seized Zeidan "on the prosecutor's orders".
The premier "was arrested under the Libyan penal code... on the instructions of the public prosecutor", the group said.
It said he was detained for "crimes and offences prejudicial to the state" and its security.
The cabinet said on its Facebook page that ministers were "unaware of immunity being lifted or of any arrest warrant" for the prime minister.
Zeidan's detention comes five days after US commandos embarrassed and angered Libya's government by capturing senior Al-Qaeda suspect Abu Anas al-Libi off the streets of Tripoli and whisking him away to a warship.
At the time, the Operations Cell of Libyan Revolutionaries ordered its fighters to be prepared for orders to "hunt down and expel foreigners who are illegally in the country".
It said it was on high alert "in light of the deterioration in security and damage to the country's sovereignty by foreign intelligence bodies".
NJF/NJF