Fans from the opposing teams, US Ouakam and Stade De Mbour, exchanged blows and numerous projectiles were fired, Senegal's official news agency Agence de Presse Senegalaise (APS), reported.
As spectators tried to leave the stadium, APS said a wall collapsed under their weight.
Ambulances and fire trucks were dispatched to attend to the victims, while police used tear gas to disperse the large crowd.
Senegal's President Macky Sall said on Twitter
that those behind the tragedy would be punished.
"Outraged by the incidents at the Demba Diop Stadium. The light will be cast on this tragedy. Those responsible will be identified and sanctioned," Sall said in French.
Other stadium stampedes
The incident in Senegal is the latest in a list of stadium disasters around the world this year.
Earlier this month, eight people were killed at in a stampede at the Bingu National Stadium in Lilongwe
as people arrived to celebrate Malawi's 53rd anniversary of independence.
In May, four people were killed and several injured in a stampede at Honduras' national stadium prior to the league final between Motagua and Honduras Progreso.
Police said a group of fans had tried to enter one section of the stadium in a violent manner.
, at least 17 people were killed ahead of the opening match of the football league in February.
The stampede happened at the Municipal Stadium 4 de Janeiro, which is in Uíge, some 300 kilometers (186 miles) northeast of the capital, Luanda, state-run media reported.
State-run television station TPA reported football fans did not follow security instructions and tried to enter the stadium through one gate to watch the match between Santa Rita de Cássia and Recreativo do Libolo.