Dave passed away at his official residence here. The exact time is not yet known. The incident came to light at around 7.30 a.m., when his staff tried to wake him up.
"Absolutely shocked by the sudden demise of my friend and a very respected colleague, Environment Minister Anil Madhav Daveji. My condolences," Modi tweeted.
"He will be remembered as a devoted public servant. He was tremendously passionate towards conserving the environment," said Modi.
"I was with Anil Madhav Daveji till late last evening, discussing key policy issues. This demise is a personal loss," he added.
Dave's death was confirmed by family friend, Meena Agarwal. She said: "His body will be taken for embalming. And will be later taken to Indore."
Dave was born in Badnagar in Madhya Pradesh. He has been a member of the Rajya Sabha since 2009. He was sworn in as a Minister of State with independent charge of Environment, Forest and Climate change in 2016.