Singh had on Monday accused the party's state leadership of letting him down by "violating" his self-respect after denying him a ticket from Nawada, a seat which he won in 2014.
The BJP has announced Singh as its candidate from Begusarai this year.
Extending best wishes to Singh, Shah in a tweet said he has heard all the issues raised by the Union Minister and "all his problems will be resolved by the party."
"Giriraj Singh will contest from Beghusarai only," Shah tweeted.
BJP is contesting on 17 out of 40 Lok Sabha seats in Bihar. An equal number of seats are being contested by its ally JD (U).
It’s another partner LJP is contesting on the remaining seats.
As per the seats arrangement between the three parties, the Nawada seat has been given to the to Ram Vilas Paswan’s Lok Janshakti Party.
The union minister's “reluctance” to contest the Lok Sabha election from Begusarai was comparable to a kid’s refusal to attend school after failing to complete homework, CPI candidate and former JNU students’ union president Kanhaiya Kumar said on Tuesday.
The Begusarai seat has been lying vacant since the death of sitting BJP MP Bhola Singh in October last year.
Earlier, the Grand Alliance of the Rashtriya Janata Dal (RJD), Congress and other parties did not allocate Begusarai to the CPI.
The RJD is set to field Tanweer Hasan who lost to Bhola Singh of BJP in 2014.
Kanhaiya Kumar has said that his fight will be against Giriraj Singh, not RJD. He has appealed to people to donate at least 1 rupee for his campaign fund.
(With inputs from Agencies)