UPDF denies claims that its soldiers picked Lual Malong Jr from a hotel.
Mr Lual Malong Yor Jr's family filed a report at Kabalagala Police Station in Kampala.
Family claims he was picked up by military men from his hotel room.
Uganda police are investigating the circumstances under which a South Sudanese “tycoon”, popular for flaunting dollars on social media, went missing last Wednesday.
Kampala police spokesman Luke Owoyesigyire told the Daily Monitor that the family of Mr Lual Malong Yor Jr filed a report at Kabalagala Police Station on Wednesday saying they had not heard from him since November 14.
The family claims Mr Malong was picked up by people in military uniform from his hotel room in Kabalagala, a Kampala suburb.
“His brother reported [the matter] to police. I can confirm he is not in our custody," Mr Owoyesigyire said.
He said the police is carrying out investigations and is liaising with other security agencies.
News of Mr Malong’s disappearance was first reported on Wednesday by Juba-based Radio Tamazuj.
The station quoted a relative as saying: “(The) hotel 'guys' said Lual was picked up by UPDF soldiers who came in two vehicles, but the UPDF has denied [the claim]."
“We do not know who abducted him from the hotel. What we know is that Lual has no problem with the government of Uganda. We are very concerned as his family members,” the relative told Radio Tamazuj.
Reached for comment, the Uganda People's Defence Force spokesman Brigadier Richard Karemire said the army was not holding Mr Malong.
“I have no information about that individual being held by the UPDF,” he said.
The family and police have not revealed which hotel Mr Malong is alleged to have been picked up from.
Mr Malong shot to the spotlight in October when he posted a video online of himself lying on wads of US dollar bills claiming he would be donating it to charity.
He says he is not the son of former head of South Sudanese army, Gen Paul Awan Malong.