The men, who were travelling on South African passports, were found guilty on weapons and immigration charges related to the plot.
Zimbabwe's high court last week reduced their sentences by four months following an appeal, qualifying them for immediate release.
The South African Broadcasting Corp (SABC) radio said Zimbabwe's Attorney-General Sobuza Gula-Ndebele had filed an application with the Supreme Court to overturn the ruling, saying only Zimbabweans qualified for a suspension of a prison term.
"In our view, the suspended sentence is for locals, people who are under Zimbabwean jurisdiction ... but in relation to foreigners, that becomes superfluous because we don't control foreigners," he said.
Under Zimbabwe's laws, prisoners are entitled to serve two thirds of their jail terms if they behave well in custody.
Equatorial Guinea sentenced 11 foreigners in November to between 14 and 34 years in jail for their role in the plot, and two of its own citizens to 16 months in jail.
In South Africa, a son of former British prime minister Margaret Thatcher, Mark Thatcher, pleaded guilty in January to a role in the foiled plot under a plea bargain to avoid prison.
Earlier on Tuesday, South Africa's National Prosecuting Authority said the 62 men could still face charges at home.