A press release from the French club read: "Leonardo today informed Paris Saint-Germain of his desire to resign from his position as sport director at the end of the current transfer window.
"We regret his choice but respect his decision. We thank him greatly for his important contributions towards the project of building a top European club in Paris and wish him all the best for his future career choice."
Last week the Brazilian learned he would be banned from the touchline and match officials’ areas until June 30, 2014, having appealed against a more lenient ban that ran for nine months.
Leonardo incurred the punishment after pushing a referee following a Ligue 1 match against Valenciennes in May.
PSG said "the club deplores the severity of the new, harsher penalty" and added that they would be considering their legal options upon receiving the written reasons for the ban.
Leonardo was appointed as PSG sporting director in July 2011 following spells as coach of AC Milan and Inter and helped establish the French club as a European force through some ambitious acquisitions in the transfer market.