Djermakoye was preparing to speak to the crowd in intense heat when he was taken ill, one of his aides said.
The former minister, who had been known to have been suffering from a heart condition, later died in hospital.
A constitutional court in the West African nation had already ruled on Friday that a decree by Tandja calling for the referendum was illegal.
"The court's decision is a victory but we should not lower our guard," Mahamadou Issoufou, head of the opposition Nigerien Party for Democracy and Socialism (PNDS), which has been leading the campaign against the referendum, said in a speech to the protesters on Sunday.
"With the court ruling, any order given to go ahead with the referendum will be illegal. President Tandja must submit to this," he said, speaking before Djermakoye's death was announced.
Tandja has said that he needs an extra term in order to implement a fully-presidential system of government and to see though large infrastructure projects.
The US government said that a referendum would be a set back to democracy.
The Economic Community of West African States (Ecowas) said that they could impose economic sanctions if Niger acts in an undemocratic way.