Rwandan police also posted a message on Twitter saying Rwigara and members of her family were held on Sunday for not responding to summons and were later released.
"They are accused of tax evasion, and secondly Diane Rwigara is accused of using fake documents while she was gathering signatures for (her) presidential candidacy," Theos Badege, police spokesman, told reporters on Monday, according to local media reports.
"They have been brought to CID for questioning, after refusing to respond to three summons as stated by the law. After questioning at CID, Anne Rwigara, Diane Rwigara and Adeline Rwigara were escorted home by the police."
Her friends and family say Rwigara is being persecuted for holding different views and championing Rwandans' rights.
Rwigara, 35, was the only female challenger in last month's elections, which Kagame won by a landslide 98.8%.
In an interview with CNN
in the lead up to the elections, she said her candidacy had been targeted, first by the leak of nude photos that she said were fake.
Rwigara also was disqualified from standing in the elections by the country's electoral commission who accused her of submitting names of dead people and not gaining enough signatures from supporters. Rwigara vigorously denied the allegations.
A former military strongman praised for turning around the country's fortune, Kagame enjoys huge popularity in the country, which has seen strong economic growth in recent years and improved standards of living.
Critics argue the successes of Kagame's tenure have come at a high cost for civil society.
"Two decades of attacks on the political opposition, independent media and human rights groups have created a climate of fear," a recent Amnesty International report said.
At the time Rwigara told CNN
she was not fearful of the consequences of criticizing President Kagame.
"When a hyena runs after you long enough you end up losing fear," she said, quoting a Rwandan proverb. "Living in fear is not life."
But she admitted to feeling frustrated by "the way things are in this country -- we are not allowed to talk about the many challenges."
Rwanda currently leads the world in terms of share of female legislators -- 61% of the country's parliament are women -- but female presidential candidates haven't been as successful.
In 2003, Alvera Mukabaramba made a bid for the presidency but later withdrew and joined forces with Kagame. She ran again in 2010 alongside another woman, Victoire Ingabire, a Netherlands-based Hutu lawyer who returned to Rwanda to stand in the elections.
Ingabire ran into trouble over comments she made about the country's 1994 genocide and was later sentenced to 15 years in prison
for treason and "denying genocide."