The protesters, mostly youths, gathered near the presidential palace carrying Sudanese flags and signs reading "The army is Sudan's army" and "Don't dismiss the army's free men".
They burned tyres and blocked roads, before police fired tear gas to disperse them, an AFP correspondent said.
Earlier this week, the military published a list of officers of various ranks who had been forced into retirement.
Army spokesman Brigadier Amer Muhammad al-Hassan, quoted by state news agency SUNA, said the list was issued "as usual at the beginning of each new year".
Hassan told AFP that the army's code of conduct bars soldiers from taking part in political activities.
"There's no place in the armed forces for anyone who is promoting any political activity. This is a directive from the leadership," said Hassan.
But activists launched a social media campaign backing sidelined Lieutenant Mohammad al-Sadiq, who had voiced support for their campaign from the outset in December 2018 over soaring bread prices.
The Sudanese Professionals Association (SPA), the umbrella group which led mass street protests that led to president Omar al-Bashir's downfall in April, organised Thursday's demonstration.
SPA on its Facebook page condemned the police's "excessive use of force and repression" and urged Prime Minister Abdalla Hamdok to immediately fire the interior minister and senior police officials.
Bashir's ouster after 30 years in power led to months of talks that eventually produced a transitional government comprised of civilian and military officials.
Months of anti-Bashir protests triggered clashes with security forces that left dozens dead, hundreds wounded and thousands jailed.