The Council for Cultural Revolution, a high-ranking body chaired by President Mahmoud Ahmadinejad, dismissed him on Tuesday night, state media said.
Mr Mousavi had run the institution, affiliated to the president's office, since its inception 11 years ago.
In recent days, hardliners have urged Iran's judiciary to put Mr Mousavi on trial for instigating unrest.
Mr Mousavi came second in the June election, and anger at the result saw mass protests in Tehran and other cities that led to thousands of arrests and some deaths.
Mr Mousavi has said the poll, that returned President Ahmadinejad to power, was fraudulent.
News of Mr Mousavi's sacking comes a day after his car was reportedly attacked as he travelled back to Tehran from the holy city of Qom, where he had joined tens of thousands for the funeral of a dissident cleric, Grand Ayatollah Hoseyn Ali Montazeri.
An earlier report suggested that the Arts Institution job was Mr Mousavi's only public post, but he also remains on the Expediency Council.
This is seen a key body within the Iranian politics and at times a forum for reconciling legislation when debate in the legislature becomes deadlocked.