"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?"
Winnie Byanyima is a human rights advocate and executive director of Unaids, the joint UN programme which was set up to eradicate Aids.
Kizza Besigye used to be Museveni's personal doctor but he went on to become an opposition leader and has referred to 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.