The two have allegedly spread misinformation about Rahul, who is now the Leader of Opposition, and his mother.
Chaudhary has been accused of posting on social media that Sonia Gandhi, an Italian by birth, is still a Christian despite marrying in India.
Sonia, a former and the longest serving Congress president, was married to ex-Prime Minister Rajiv Gandhi.
She has also been linked to the Pakistani intelligence agency ISI.
Rahul, also an ex-Congress chief, has been accused of meeting a Bangladesh National Party leader and sexually assaulting a woman in London.
The complaint over the journalist's accusation has been lodged by G Srinivas, who is a member of the Karnataka Pradesh Congress Committee.