Prajwal Revanna, the lawmaker, had been out of the country since the accusations surfaced last month and was arrested on his arrival in the southern city of Bengaluru, capital of Karnataka state.
The state government formed a special investigation team to probe the accusations of sexual harassment against Revanna after obscene video clips were circulated days before the state voted in national elections on April 26.
He is seeking a second term from his Janata Dal (Secular) party in the seven-phase election which ends on Saturday.
Revanna, the grandson of former Prime Minister H.D. Deve Gowda and nephew of a former Chief Minister of Karnataka, arrived in Bengaluru a week after his grandfather urged him to return and face the law.
Revanna faces three cases filed by several women, local media has reported.
In a video clip aired this week, the lawmaker apologized to his family, people of the state and party workers.
"I am confident I will emerge from these false cases through the court," he said.
On May 1, Revanna said on social media that he was out of the country and needed time to return to join the investigation, adding that "truth will prevail soon".
His father and former Karnataka minister H.D. Revanna was also arrested in a kidnapping case filed by the son of one of the women linked to the harassment case and who had gone missing, local media reports said. He has since been released on bail.
Both father and son have said the cases are a part of a political conspiracy against their family.
The case became a flashpoint in the ongoing elections, with opposition leaders criticizing Modi and his government for allowing Revanna to flee on April 26 after allegations surfaced.
In a television interview aired this month, Modi said that the case is a "law and order issue" and "there should be stringent action" against the culprits.