The man's condition is not critical, according to DR Nyheder.
The shooting incident occurred during the early hours of Monday on the Edwin Rahrs Vej road in the western part of the city.
East Jutland police vice inspector Jeppe James Olsen told DR that the shooting is being considered as related to an ongoing gang-related conflict in the west Aarhus neighbourhood.
Several arrests were also made last weekend after a series of violent incidents in the area.
Police received new reports of shootings at an address in west Aarhus just after midnight on Monday.
“We dispatched a patrol to the location, but did not find anyone there. But shortly afterwards a 21-year-old man with gunshot wounds was brought in to the hospital. He has been treated overnight and his life is not in danger,” Olsen said.
“We are working on several theories, but initial impressions suggest that this is an internal conflict in an ongoing organised crime conflict in west Aarhus,” he added.
Police are reported to believe the recent surge in organised crime-related violence in Aarhus to be linked to attempts by a Copenhagen-based gang known as ‘Loyal to Familia' to establish itself in the city.