The president's son, Lt Col Kainerugaba Muhoozi, who already commands a special forces unit, has now been given control of the elite presidential guard.
"He's making the Ugandan presidency a monarchical affair and is clearly anointing his son to succeed him," said opposition spokesman Hussein Kyanjo.
Several of Mr Museveni's relatives hold senior positions in his administration.
His wife was appointed to the cabinet last year.
Army spokesman Felix Kulaigye dismissed the criticism of the latest appointment.
"Muhoozi didn't commit any crime by being the son of the president. He's an individual Ugandan with rights including contesting for the presidency if he wants," he said, reports the Reuters news agency.
Lt Col Muhoozi, 36, was appointed head of the special forces unit in 2008. He has had military training in both the UK and US, reports the AFP news agency.
Mr Museveni, in power since 1986, is expected to seek re-election next year.
He changed the constitution to be allowed to stand in the 2006 polls.
Mr Kyanjo's Forum for Democratic Change said those polls were rigged - charges denied by Mr Museveni.
KEEPING IT IN THE FAMILY?
Gen Caleb Akandwanaho - Mr Museveni's brother - senior presidential advisor on defence
Sam Kutesa - brother-in-law - foreign affairs minister
Janet Museveni - wife - minister for Karamoja region
Lt Col Kainerugaba Muhoozi - son - commander of special forces
Natasha Karugire - daughter - private secretary to the president
Hope Nyakairu - relative of first lady - finance under secretary at state house
Justus Karuhanga - first lady's nephew - president's private secretary for legal affairs
Mensagens
