A social media post by his social media administrator said Wine was whisked to an unknown destination.
Police would later counter this saying they only escorted him from the Airport to his home in Magere.
They termed the reports of his arrest as rumours.
The arrests happened as President Yoweri Museveni presided over the national Independence Day celebration at Kololo Ceremonial grounds.
Uganda earned sovereignty after 70 years under British control.
On this day in 1962, Uganda was officially declared a free state among the international community.
Kyagulanyi who is a fierce critic of Museveni is set to make yet another attempt to succeed Museveni in the next presidential elections.
The elections are scheduled to be held between January 12 and February 9, 2026.
He has lined up a series of mobilisation tours across the country which will be coupled with the opening of new offices for the National Unity Platform party on whose ticket he would likely be seeking the top seat.
The first phase of the mobilisation tours started on August 28 and will run until September 13 across 10 districts.
"We shall go out to address our people physically and on media houses, and officially open our offices," Wine said in a statement on August 23.
The start of the tours came at the end of a two-day retreat of the National Executive Committee of the National Unity Platform party.
