Lee last week called for Gilbert's sacking after the NSW board had axed coach Anthony Stuart.
NSW responded to the media comments by reporting Lee, who is retired form the Blues and now only plays for the Sydney Sixers in the Big Bash.
Lee is alleged to have breached rule six for unbecoming behaviour and rule nine for detrimental public comment.
Under the code of conduct, players must not bring the game into disrepute or be harmful to the interests of cricket.
Lee said the blame for NSW poor State cricket form was unfairly heaped on Stuart and that CEO Gilbert deserved to have questions asked of his performance.
The fast bowler questioned Gilbert's leadership and said he should have been the man to go instead of Stuart.
The date and time of the Cricket Australia hearing is yet to be confirmed.