Yoweri Museveni has vowed to rid the East African country of corruption.
Besigye is being held in Uganda's only maximum security prison.
The police have denied they were involved and accused Mbabazi of "dirty tricks."
President Yoweri Museveni was re-elected in a controversial presidential election in February.
The international community responded in a variety of ways to Museveni's re-election.
President Yoweri Museveni won Thursday's controversial elections with 61 percent of the vote.
Despite the blackout, #UgandaDecides is still trending.
President Museveni said anyone trying to stir up violence ahead of the polls would be dealt with harshly.
Most Ugandans have never known a president other than Yoweri Museveni.
Besigye is the main challenger to Yoweri Museveni in Thursday's elections.
Amama Mbabazi has pledged to return Amin's remains to Uganda if he is elected.
David Sejusa, a prominent critic of the Ugandan president, has been charged with military offenses.
The Ugandan president spent 12 times more than his two closest opponents combined in November and December.
Museveni is standing against his former doctor and a former prime minister in February's elections.
Ugandans go to the polls in February as Yoweri Museveni seeks to extend his 30-year rule.