Opponents say Narendra Modi should undergo an investigation to determine whether he lied in past elections.
The Congress Party lodged the complaint with India's Election Commission, asking why Modi had failed to declare he was married while contesting earlier elections.
Copngress is widely expected to lose the coming election to the opposition Bharatiya Janata Party (BJP), which has made Modi its prime ministerial candidate.
Modi, 63, publicly acknowledged for the first time on Wednesday that he was married decades ago by filling in the name "Jashodaben" in the spouse section of his nomination papers in Gujarat, the state he currently governs.
In all previous elections he has contested, Modi left the field for the name of the spouse blank. His team insists no deception took place, as the two have not lived as man and wife for years, even if no divorce ever took place.
"The affidavits he filed earlier are all false. We have complained to Election Commission about the same and asked for a probe," Congress minister Kapil Sibal said at a news conference.
"It is a matter of concern as he is an aspirant for the office of prime minister," he said.
"If he didn't give information about his marital status, we are a little concerned how then do we put the trust of the nation in his hands, there may be many other things that he may have not disclosed."
Modi, who has been chief minister of the western state of Gujarat since 2001, is generally described as a bachelor.
He took a vow of celibacy when he joined the Rashtriya Swayamsevak Sangh (RSS), a right-wing Hindu nationalist organisation, as a preacher. The RSS is the ideological fountainhead of the BJP.
"Narendra was married to Jashodaben Chiman Modi at a very young age by our parents, but it was only a formal ritual," Indian media quoted Modi's older brother Sombhai Modi as saying on Thursday.
In a February interview with Indian Express newspaper Jashodaben had said she and Modi were together for three months after their marriage and that he left her after three years.
She had also said they parted amicably and that she did not want anything from him.
The BJP leader has been leading opinion polls in the run-up to India's five-week-long general elections that end on May 12.
He is seen as an efficient administrator but his image has been sullied by deadly Hindu-Muslim riots in Gujarat in 2002 during his first tenure as chief minister.