Arun Narayan and Musafir Baitha, both assistants in the department of Hindi publication, are also facing departmental inquiry over the episode.
They were suspended by Council chairman Tarakant Jha, a Bharatiya Janata Party (BJP) leader.
Jha admitted the two had been suspended for writing against the government on Facebook but provided no details.
According to one official, they violated service rules.
Narayan, who regularly writes in Hindi dailies and magazines, had commented against the termination of rebel Janata Dal-United's Prem Kumar Mani from the Bihar Legislative Council.
Baitha was accused of initiating a discussion on Facebook about how administrative lethargy in the Council had caused suffering to employees.