Videos showed screaming fans being crushed at an entry gate to the Olembé stadium in the capital Yaoundé.
Witnesses described chaotic scenes outside the ground as thousands of fans struggled to get access.
Two boys, aged eight and 14, are among the dead, and seven people were seriously injured.
Cameroonian President Paul Biya ordered an investigation into the "tragic incident". The Confederation of African Football (Caf) has also launched its own investigation, and says a minute's silence will be observed at future matches as a mark of respect to those who died.
Officials say about 50,000 people tried to attend the match on Monday.
The stadium has a capacity of 60,000 but it was not meant to be more than 80% full for the game because of Covid restrictions.
Nick Cavell, a producer for BBC Africa Sport, was at the match and says news of the crush did not seem to filter through to the crowd until there were reports on social media.
Images on social media show fans clambering over fences, rushing past checkpoints and trampling on unconscious supporters. Others show some trying to resuscitate their fellow fans.
Danish journalist Buster Emil Kirchner described seeing "a lot of chaos" as fans clamoured to enter the ground through a single open gate.
"It was hectic - people running, people climbing fences, people breaking through the barricades," he told the BBC.
Another journalist, Leocadia Bongben, saw a commotion coming from one of the fan zone areas outside the stadium.
"People started shouting," she told the BBC's Newsday programme. "A minute after that an ambulance came to the stadium, but when we got to the place the police would not allow us to get close to where the stampede was.
"It's really quite a sad situation that people go to watch a game and they end up dying there."
Some of the injured were in a "desperate condition", nurse Olinga Prudence told the Associated Press.
Vanessa Tchouanzi told Reuters news agency she saw her friend get knocked over and killed by a rush of people "coming in in droves".
"She couldn't take the shock, the weight of all those people," she said.
Football's world governing body Fifa said the "thoughts and prayers of the global football community" were with those affected.
Caf President Patrice Motsepe said no more tournament matches would take place at the stadium until there was an "absolute guarantee" fans would be safe.
"Clearly there were failures - there were things that should have been foreseen," Mr Motsepe told a press conference.
The African football body said Sunday's quarter-final would now be moved from the Olembé stadium and held instead in another stadium in the same city - the Ahmadou Ahidjo.
