The market is near one of the main camps in the Sudanese capital, where the paramilitary Rapid Support Forces (RSF) have been fighting the military as part of a civil war that has killed tens of thousands of people.
"Twenty-three people were confirmed dead and more than 40 others wounded" and taken to hospital after "military air strikes on Saturday afternoon on the main market" in southern Khartoum, the youth-led Emergency Response Rooms said in a post on Facebook.
Fierce fighting has raged since Friday around Khartoum, much of which is controlled by the RSF, with the military pounding the center and south of the city from the air.
The military is advancing towards Khartoum from nearby Omdurman, where clashes erupted on Saturday, eyewitnesses said.
World's largest displacement crisis
The World Health Organization says at least 20,000 people have been killed in the civil war, but some estimates put the toll much higher at up to 150,000.
The war has also created the world's largest displacement crisis, the U.N. says.
More than 10 million people, around a fifth of Sudan's population, have been forced from their homes, according to U.N. figures.
A U.N.-backed assessment in August declared a famine in the Zamzam refugee camp in Darfur near the city of El-Fasher.
The government loyal to the army is based in Port Sudan on the Red Sea coast, where the army has retained control.
The RSF meanwhile has taken control of nearly all of the vast western region of Darfur, rampaged through the agricultural heartland of central Sudan and pushed into the army-controlled southeast.