The 60-year-old minister complained of uneasiness at his home this morning and was rushed to AIIMS where he passed away, according to official sources.
He was sworn as minister with independent charge of environment, forest and climate change last year. He was a member of the Rajya Sabha since 2009.
Dave was a bachelor.
He had a long time association with the Rashtriya Swayam Sewak Sangh and shot into prominence in 2003 when he crafted the strategy leading to the defeat of Chief Minister Digvijay Singh.
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Prime Minister Narendra Modi also condoled the death of Dave.
"Absolutely shocked by the sudden demise of my friend & a very respected colleague, Environment Minister Anil Madhav Dave ji. My condolences," he said in a tweet.
The Prime Minister said Dave will be remembered as a devoted public servant who was tremendously passionate towards conserving the environment.
"I was with Anil Madhav Dave ji till late last evening, discussing key policy issues. This demise is a personal loss," he said in another tweet.
Home Minister Rajnath Singh said he was saddened to learn of the demise of the minister.
Finance Minister Arun Jaitley also expressed grief over the demise of Dave.