Lt-Gen Kainerugaba is among more than 2,000 military officers who were promoted, according to the list released by the UPDF on Friday.
The 44-year-old First Son moved up to the rank of Major General in 2016 and a year later appointed as the Special Presidential Advisor for Special Operations.
He was previously head of the elite Special Forces Command, a unit in charge of the president’s security.
Also promoted on Friday is Uganda’s only woman Maj-Gen Prossy Nalweyiso to Lt-Gen.
The Deputy Inspector General of Police Sabiiti Muzeyi moved up to Maj-Gen from Brigadier.
“The President and Commander-in-Chief of the Uganda Peoples’ Defence Forces has confirmed the promotions of 2,031 UPDF personnel to various ranks,” read the statement by the army.
The promotions have seen two officers become full Generals, 10 move up to Lt-Gen, 16 to Maj-Gen, and 35 to Brig.
The preferment of Museveni’s son is likely to trigger debate on his succession plan with some observers saying Lt-Gen Kainerugaba could be a potential successor given his rapid rise through the army ranks since joining 20 years ago.
President Museveni, in power since 1986, is, however, largely expected to seek a sixth term in 2021 election.