The stampede occurred when gates were opened at the 40 000-seat Bingu stadium in the capital Lilongwe for a presidential address and football match to mark the annual holiday.
“Eight people – seven children aged around eight years old, and one adult died,” national police spokesperson James Kadadzera told AFP.
He said 62 people were injured and hospitalised.
“My government will do all it can to assist the bereaved families,” President Peter Mutharika said at an independence day prayer meeting. “We are mourning with you.”