Shah belongs to the royal family of the erstwhile Tehri princely state.
The Tehri Garhwal seat had fallen vacant when Vijay Bahuguna resigned on July 23, 2012 to become Chief Minister of the state.
Shah's name was recommended for the by-election by BJP Uttarakhand unit headed by Bishan Singh Chufal. The BJP state election committee had also recommended the name of former Uttarakhand Chief Minister B C Khanduri and Dehardun Mayor Vinod Chamoli among the probable candidates.
The by-election will be held on October 10.