"Kirti Azad-hero of the day," the outspoken actor-turned-politician tweeted.
"Humble appeal to friends. Avoid knee jerk reaction/coercive action against (a) friend who's fighting against corruption.
"Have often quoted Newton's 3rd Law. Feel that untimely action could boomerang. Sadly, Party With a Difference has become Party With Differences."
Sinha had a piece of advice for Jaitley, who headed the Delhi and District Cricket Association (DDCA) for 13 years till 2013.
"As for FM (finance minister), (the) issue should be fought politically not legally.
"As advised by our dashing dynamic PM, our FM could follow Advaniji's example and come clean."
Veteran BJP leader L.K. Advani had declined to contest elections when he was accused of involvement in the hawala scandal in the 1990s.
On Tuesday, Prime Minister Narendra Modi had said that Jaitley would come out of the DDCA row with flying colours -- a la Advani.
Sinha's support for Azad came a day after senior Bihar BJP leader Sushil Kumar Modi demanded disciplinary action against Azad for targetting Jaitley over the DDCA issue.
Cricketer-turned-politician Azad is a BJP MP from Darbhanga in Bihar and the son of former Bihar chief minister Bhagwat Jha Azad.
Sinha is the BJP MP from Patna Saheb in Bihar.