Patel, 55, complained of chest pain at home following which he was rushed to a private hospital in Rapar town where he died, they said.
He had defeated Congress strongman Babu Shah in the 2012 Assembly elections.
Patel was the chairman of Rapar Area Development Authority before contesting elections on the saffron party ticket.
Gujarat Chief Minister Narendra Modi expressed grief over his demise.
"Vaghajibhai Patel will be remembered as a committed leader and a dedicated MLA. Condolences to his family on his demise. RIP (Rest In Peace)," Modi wrote on micro-blogging site Twitter.
In addition, there are two GPP and NCP legislators each, one JD(U) MLA and one independent MLA in the House.
Patel's demise will necessitate a by-election for the Rapar Assembly seat in Kutch district.