Supporters of the imprisoned opposition leader staged a protest at the court.
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.
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.
Besigye, Uganda's main opposition presidential candidate, was briefly detained on Monday.
Amama Mbabazi has pledged to return Amin's remains to Uganda if he is elected.
Museveni is seeking re-election on February 18 after 30 years in power.
David Sejusa, a prominent critic of the Ugandan president, has been charged with military offenses.
Uganda's former prime minister has ultimately failed to convince voters that the time for change is now.
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 and opposition activists are reportedly being targeted.
Ugandans go to the polls in February as Yoweri Museveni seeks to extend his 30-year rule.
Voters go to the polls in February, with President Yoweri Museveni looking to extend his 29-year rule.