A statement issued by the Ghana Armed Forces said Wednesday's "tragic" incident was caused by an "unexpected influx of applicants who breached security protocols and forced their way through the gates."
Twenty-two others were injured, five of whom remain in critical condition.
Thousands of people had gathered at El-Wak Stadium in the capital, Accra, hoping to join the army.
Ghana's youth unemployment rate is around 32%, according to the latest government data, and such recruitment events typically draw large crowds and often lead to chaos.
The deadline for applying for the program was extended by a week to accommodate more applicants, as some applicants encountered difficulties in the process.
Army spokesperson Captain Veronica Adzo Arhin said the gathering occurred before the scheduled time of 06:20 GMT.
Ghanaian President John Mahama visited the injured in hospital.
Calm has been restored and the recruitment process has now begun.