Singh had posted pictures of top Bihar NDA leaders, including Chief Minister Nitish Kumar and Union minister Ram Vilas Paswan, attending 'Iftar' and questioned as to why people lag behind in observance of their own "karm-dharm" (religious customs) while staying ahead in making a show for religious rituals of others.
BJP leader and Bihar Deputy Chief Minister Sushil Modi was also seen in one of the pictures.
His tweet drew sharp reactions from the BJP allies. A BJP leader said Shah admonished Singh and asked him to avoid making such remarks.
"Why we lag behind in our religion and rituals and lead in display for other," Giriraj Singh tweeted, saying the picture would have been beautiful had 5they organised "phalahar on Navratra".
Singh posted the comment along with a picture of Nitish Kumar, Paswan, Bihar Deputy Chief Minister Sushil Kumar Modi holding each other's hands at the iftar here on Monday.
JD-U spokesperson Sanjay Singh did not like Singh remark and reacted demanding action against the Begusarai MP.
"It is high time BJP should take Giriraj Singh's statements seriously and act against him as PM Narendra Modi had recently stated that he would check and control all such leaders of his party who speak the language of hate," the Janata Dal-United leader said.
Nitish's JD-U and Paswan's Lok Janshakti Party are allies of the Bharatiya Janata Party.
Having returned to the NDA two years ago, Kumar has however been insistent on the JD(U) maintaining a distinct ideological position, often at variance with that of the BJP.
(With inputs from agencies)