Lise Thibault, who held the provincial vice-regal post between 1997 and 2007, is charged with fraud and breach of trust in relation to hundreds of thousands of dollars in expense claims.
Lower courts have rejected her argument that as the Queen's representative she is not subject to the criminal justice system on the principle that the Crown can do no wrong.
Thibault is to go on trial next April.
She also faces a civil suit brought by the province.
As usual, the Supreme Court gave no reasons for refusing to hear the case.