"In what capacity has he (Modi) asked for my expulsion?" Sinha said in a series of tweets.
"Before casting aspersions, he must look within himself and his diminished personality and performance," Mr Sinha said in an apparent attack on Mr Modi without naming him.
Mr Sinha said it was high time and right time that "he must learn a lesson - or be taught a lesson by our party high command".
Mr Sinha's remarks came two days after the two Bharatiya Janata Party leaders sparred on Twitter as the actor tweeted in favour of RJD chief Lalu Prasad and Delhi Chief Minister Arvind Kejriwal.
Mr Sinha had called for an end to "negative politics and mudslinging", after Kejriwal and Lalu Prasad came under attack following corruption charges in different cases.
Former Bihar Chief Minister Sushil Modi, responding to Mr Sinha's tweet, had demanded that the "enemies of the party" (Sinha) must be "removed" at the earliest.
Criticising Mr Modi for using un-parliamentary language, Sinha said: "I am being swamped by messages from senior political leaders, colleagues, well wishers and friends who are shocked by the unparliamentary and undignified outburst from our so-called matured and senior political colleague from Bihar."
Mr Sinha also said that there could be little justification for stooping to such a level as calling names to a long time political colleague and respected party senior, breaching all decorum.
Lashing out at Mr Modi, Mr Sinha said, "Frustration, desperation or loss of face in political defeat cannot justify such utterances - it appears to be a more deep-rooted complex".
Mr Sinha, who represents Patna Sahib constituency of Bihar, said: "It is not even the case of a pot calling the kettle black...since I am no kettle!"
"He must understand that many people within the party and outside have appreciated my concerns, patience, principles and dignity and the majority have criticised him not only for his utterances,
"But also for bringing a bad name to our party and it's leaders by being fully responsible for the disastrous result in Bihar," Mr Sinha said highlighting the party's debacle in the 2015 Bihar Assembly polls.
"And this person (Modi) today has the audacity and the cheek to call me names in public - "And Oh My God! What a title, what a name..shame shame," he said.
"As for me, I am still fond of him, and can only wish him luck and give him good wishes for the future. God bless! Jai Bihar! Jai Hind!!" Sinha said.
Mr Sinha has been criticising the central government led by Prime Minister Narendra Modi since the 2015 Bihar polls after he was sidelined in the party.
He has backed Bihar Chief Minister Nitish Kumar and Mr Kejriwal on several occasions.