A wall collapsed at Demba Diop stadium as people attempted to leave after the game between local teams Ouakam and Stade de Mbour.
In the crush, police started firing tear gas to disperse the crowd, causing further panic.
At least 17 people died and scores were injured in a stampede in a match in Angola in February, when hundreds of supporters stormed the stadium.
Pictures were posted on social media appearing to show fans climbing over a low wall, with gas clouds in the air.
Police said a group of fans had tried to enter one section of the stadium in a violent manner.
The minister vowed "strong measures so that such an event will never be repeated in Senegal".
"All of a sudden the wall fell. we knew exactly that some of our own had lost their lives because the wall fell directly onto people", said Cheikh Maba Diop, an eye witness.
The government also announced a ban on sports and cultural activities during the legislative campaign period leading to parliamentary elections on July 30. The light will be cast on this tragedy.
Mara Die Diouf, a football fan present at the stadium, told the AFP news agency that policing at the stadium was inadequate.
Earlier this month, eight people died in a stampede at the Bingu National Stadium in Lilongwe as people arrived to celebrate Malawi's 53rd anniversary of independence.
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