The minister, Nicolas Hulot, an environmental activist and former television star who regularly ranked as one of Macron's most popular ministers, made the surprise announcement during a live interview on France Inter radio in which he said he no longer wanted to "lie to myself".
"I wished he had stayed", said Griveaux, praising Hulot for his work.
The 63-year-old added it was the "hardest decision in my life".
Audibly upset, Mr Hulot said on France-Inter radio that he had had enough of being forced to accept only "little steps" while Mr Macron had recruited him to lead a transformation in the state approach to the environment.
Macron's office sought to attribute the resignation to the "frustration, even exhaustion" of a ministerial novice suddenly confronted with the slow-moving machinery of government.
Despite Hulot's public denouncement of France's climate change efforts, electricity generation from renewable and nuclear power sources in France jumped in June, squeezing out fossil fuels such as coal, oil, and gas-France's grid operator RTE said earlier this month.
Despite urging the European Union to become more autonomous, Macron still called for continued talks with the USA, stating that US unilateralism didn't begin under the Trump administration, but followed on from actions taken during the Obama administration.
Hulot's exit also risks undercutting Macron's credentials as a leading campaigner internationally against climate change which has seen him adopt the catchphrase "Make our planet great again".
Now, more than a year later, Macron's environment minister has delivered his own stinging rebuke - only this time, it's Macron who came in for the condemnation. We can't have results in just one year and Nicolas Hulot knows that.
He was widely reported to be close to quitting in February after media reports that he had been accused in the 1990s of rape, which he denied.
Hulot became environment minister in May 2017, when Macron formed his first Cabinet.
French Minister for the Ecological and Inclusive Transition Nicolas Hulot leaves the Elysee Palace after the weekly cabinet meeting, on August 22, 2018 in Paris.
Hulot's resignation is an "environmental emergency", says Patrick Monfort, who studies the impact of climate change on microbial ecology at the University of Montpellier in France.
His doubts about remaining in government had grown over the summer as devastating droughts were met with a tepid political response, he said. "I have a little bit of influence".
Macron's political opponents immediately seized on the resignation.