Parrikar, who is contesting the Panaji Assembly bypoll scheduled on August 23, said the fake news shows the frustration of the opposition.
The BJP, while filing the complaint, demanded action against the persons behind it.
"An attempt has been made by circulating a distorted and false news item on social media like Facebook, Whatsapp amongst others to create falsehood, malign the image of our candidate Manohar Parrikar and misguide the electorate of Panaji constituency," said the complaint filed by Parrikar's election agent Pundalik Raut Desai.
Addressing a press meet here, Parrikar said, "The circulation of bogus news shows that the opposition is frustrated as it is not getting support from the people."
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He said the people of Panaji have always stood by the BJP and exuded confidence that this time too he will win with a huge margin.
BJP leader Siddharth Kuncolienkar, who vacated the Panaji assembly seat for Parrikar to contest, alleged that the Congress was behind it.
The Congress, however, rubbished the charge.
"The news is absolutely fake and it is being circulated by Congress party which is certain to lose its deposit," the BJP leader told PTI.
"We have been campaigning on a positive note. The party will never indulge in negative campaigning. The support which I have been receiving is tremendous," Chodankar said.
He alleged that the BJP itself was circulating the fake news so it could make an issue over it and divert the attention.
Parrikar was earlier elected from the constituency from 1994 till 2014.
Though the Congress emerged as the single largest party after the Assembly polls held in February this year, the BJP, with the support of the Goa Forward Party, the Maharashtrawadi Gomantak Party (MGP) and independents, managed to cobble up an alliance and formed the government under Parrikar's leadership.
The by-election in Panaji and Valpoi constituencies would be held on August 23.