Zene resigned as talks are taking place in Qatar's capital Doha with various rebel and opposition groups aimed at paving the way to elections after the military seized power last year.
"My willingness to serve my country finds itself at odds with parallel actions and initiatives of certain members of your cabinet and the government," he said in a letter to the president that was posted on Zene's Twitter account.
He did not refer directly to the talks but said the situation had stripped his department of its prerogatives and kept him in a "mere background role".
The presidency did not immediately respond to a request for comment.
Chad's transitional authorities signed a peace pact with more than 30 rebel and opposition factions last month in which they agreed to join a national dialogue after years of turmoil.
The vast Central African country has been under military rule since President Idriss Deby was killed on a battlefield in April 2021 while visiting troops fighting rebels, shortly after winning an election extending his 30-year rule.