"The court will decide on Thursday whether she remains in preventive custody as requested by the prosecution or is granted bail awaiting substantive trial", it said.
The police have said that they have enough evidence to begin prosecuting Ingabire.
Ingabire, a Hutu, is expected to vie for the presidency with Paul Kagame, from the dominant Tutsi minority, although the United Democratic Party (FDU) that she leads has not yet registered in Rwanda.
The FDU, which was formed in exile, has condemned the arrest, but asserted that Ingabire is still targeting the presidency.
The party said in a statment that it "condemns in the strongest terms possible the arrest this morning of the party chair ... for her views on how to bring about genuine national reconciliation and peace".
"We know that this violent arrest will not deter her determination, instead it prompts the struggle of this freedom icon to a higher level."
Ingabire, who has said that the charges are baseless, faces a jail term if convicted.
She was prevented from leaving the country last month because she was under police investigation.
Human-rights groups have criticised the government for planning the August polls while no significant opposition to Kagame's ruling Rwandan Patriotic Front (RPF) is in place.
Those opposition parties looking to establish themselves have complained of legal and administrative barriers to registration for the August 9 poll and harassment.
They have said that they may form an bloc to run against the RPF.
About 800,000 people, mostly ethinic Tutsis and moderate Hutus, died in the 1994 genocide.
Ingabire called for the the trial of those responsible for the death of Hutus in January.
The government said that the comments added up to a denial of the genocide and subsequently repeatedly questioned her.
Kagame, who has been in power since 2000, has not yet said that he will run in the elections but is expected to do so.