He did not expressly state if the military was holding him.
BBC News has asked the Ugandan government for comment.
Uganda’s Daily Monitor newspaper reported that senior members of his Forum for Democratic Change (FDC) party had gathered at Makindye military court in Kampala, expecting him to appear there.
Kenya’s state-funded human rights body, KNHRC has condemned “any form of abduction of those people who seek asylum in our country”.
Besigye, 68, led the FDC, contesting and losing four presidential elections against incumbent Yoweri Museveni, who has been in power since 1986.
“We his family and his lawyers demand to see him,” his wife wrote on X.
“He is not a soldier. Why is he being held in a military jail?”
Ms Byanyima is a human rights advocate and executive director of Unaids, the joint UN programme set up to eradicate Aids.
Besigye used to be Museveni’s personal doctor but went on to become an opposition leader and has referred to the leader of the east African country as a “dictator”.
He has alleged that previous presidential elections were rigged – a claim denied by the government.
The opposition figure has been arrested on numerous occasions in the past.
On one occasion he was shot in the hand, on another he suffered eye injuries after being doused in pepper spray.
The authorities have accused him of provoking them, and he has been charged with inciting violence.
Kenyan rights groups have voiced their concerns recently after a spate of forced deportations from the country, once regarded as a safe haven for refugees from across the region, and further afield.
Last month, four Turkish refugees were abducted by masked men at gunpoint in Nairobi and sent back to Turkey.
In July, 36 Ugandan opposition supporters who had travelled to the Kenyan city of Kisumu were deported without proper legal procedures, according to their lawyers.
