The journalists were looking into the illegal sales of government drugs and were arrested on Wednesday night.
The Ugandan government spokesman has demanded the immediate release of the team, according to Reuters news agency.
In a statement, the BBC said it had been in contact with the relevant authorities and is working to resolve the situation.
“I am yet to find out the logic why police arrested these journalists, who in my view were helping government to unearth the rot which is in the system,” government spokesman Ofwono Opondo told Reuters. “They should be released unconditionally.