Marcel Brisebois was arrested on Tuesday and later arraigned in Salaberry-de-Valleyfield, Que.
The former TV and radio personality is currently head of the Canadian Review Board Cultural Property Export, which falls under the jurisdiction of the federal Heritage Department.
Brisebois, 81, has been chairman since 2007 and was reappointed in March, effective June 27.
On its website, the tribunal says it certifies cultural property for the purpose of income tax and studies export licence applications that are refused.
Police said two of the charges are related to alleged offences between 1968 and 1971, while the two others are related to alleged offences between 1971 and 1980.
Brisebois is a member of the Order of Canada and the Legion of Honour.
Between 1985 and 2004 he was also CEO of the Contemporary Art Museum of Montreal.
The Heritage Department said it was aware of the arrest and called the allegations against Brisebois "extremely concerning."