"The unfortunate incident led to the death of six potential recruits," it said in a statement.
Twenty-two others were wounded in the stampede at the El-Wak Sports Stadium, with at least five in critical condition, Ghana military hospital official Evelyn Abraham-Kwabiah told journalists including AFP.
Five people were also injured in similar stampede in Kumasi, in the southern region of the country.
The army said in a separate statement on Wednesday afternoon that it has suspended the recruitment exercise and set up a committee to probe the cause of the "unfortunate incident".
At the 37 Military Hospital in Accra, scenes of grief and confusion unfolded as families crowded the emergency ward, desperate for news of their loved ones.
Relatives wept openly, clutching phones and identity cards, while medical teams hurried stretchers through the packed corridors.
Security officers struggled to control the swelling crowd outside the casualty unit, where dozens of people pressed against barricades for information.
President John Mahama arrived at the hospital under tight security to visit the injured, his convoy drawing even more of a crowd.
The Ghana Armed Forces said the stampede took place around 6:20 am (0620 GMT) when an unexpected surge of applicants "breached security protocols and rushed" through the stadium gates ahead of the scheduled screening.
"We witnessed a sad event today, we encountered a disaster," Mahama said.
"The violence ensued when the gates were opened for people to enter, but the youth rushed in, and sadly, some fell and were stomped on."
In addition to normal military activities, soldiers in Ghana are also tasked with targeting illegal mining operations in the gold-rich west African country.
Mahama said his government had mandated that the recruitment drive be done openly so that young people all over the country can have equal access to joining the military.
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