Mann's lawyers are expected to appeal the decision.
Jonathan Samkange, Mann's lawyer, said international law barred the extradition of people indicted in political trials or facing possible torture.
"It would be a very sad day if Zimbabwe were to extradite a man against all international conventions," he added.
Jose Ole Obono, Equatorial Guinea's attorney general told the court that although his government believed Mann was the "intellectual head" of the coup plot, he would get justice.
Zimbabwean state lawyers said Equatorial Guinea was willing to have an African Union appointed judge preside over Mann's trial and that the death sentence would not be imposed if he is found guilty.
Sixty-six other defendants arrested with Mann when their plane stopped in Harare served less than one year in jail after pleading guilty to charges of violating Zimbabwe's immigration and civil aviation laws.
Eleven others, including a number of foreigners, are serving sentences ranging from 13 to 34 years in an Equatorial Guinea jail in connection with the coup plot.
Mark Thatcher, son of former British prime minister Margaret, was accused of helping to fund the plot.
He pleaded guilty to taking part but cut a deal with prosecutors in South Africa, where he lived, to avoid jail.