Tripathi (49) died on Wednesday night due to liver-related ailment, they said.
He is survived by his wife, two daughters and two sons, his close relative and RSS worker Sanjay Mishra said.
Tripathi was elected as MP from Sant Kabir Nagar Lok Sabha seat in 2014.
Prime Minister Narendra Modi and Union Home Minister Amit Shah condoled his death.
“Shri Sharad Tripathi’s untimely demise has left me as well as many others saddened. He loved serving society and working for the downtrodden. He made unique efforts to popularise the ideals of Sant Kabir Das Ji. Condolences to his family and supporters. Om Shanti,” Modi tweeted.
Shah said Tripathi’s demise is a big loss to the party.
BJP national president J P Nadda also expressed shock and extended condolences to the deceased’s family and supporters.