Flessel, an Olympic fencing champion, cited "personal reasons" for her departure in a statement, saying she intended to renew some previous commitments, "oriented towards the human, solidarity and international cooperation".
Sources close to her said the decision had nothing to do with budgetary considerations.
Last year her ministry's budget was cut by seven percent but later granted an extra 27 million euros by a parliamentary vote.
Paris is to host the 2024 Olympics and, although the government has promised to invest one billion euros in infrastructure related to the Games, there is concern over finance in the sporting world.
Last Thursday Flessel declared a statement by French Olympic committee chairman Denis Masseglia "unacceptable" after he accused the government of a "hold-up" in relation to the sports budget.
"Thanks to patient work of consultation, we have moved from a logic of confrontation to a logic of cooperation, the only way to be ready for 2024," she said in her statement.
She stressed her loyalty to President Emmanuel Macron and Prime Minister Edouard Philippe, saying she shared "their values and their patriotism".
Still seeking einvironment minister
A reshuffle, prompted by Hulot's departure, was likely to be announced during the course of Tuesday, government sources said.
But finding a replacement for the former environment minister seems to be proving difficult.
The director of WWF France, who was development minister in the previous government, said Tuesday he would not be taking the job.
He hoped the discussions has had with government representatives would help learn the lessons of Hulot's resignation, he said in a tweet.