Marta Beatriz Roque was among the signatories
Leading Cuban dissidents have urged the European Union not to sign a trade and aid agreement with their country.
"We do not believe a country with such a black human rights record should be allowed to join" the Cotonou pact, long-time dissident Vladimiro Roca told the Reuters news agency.
Under the Cotonou pact, the EU provides aid and preferential trade to 78 African, Caribbean and Pacific countries - mostly former colonies.
Cuba applied to join the group amid warming relations with the EU.
The European Commission, the EU's executive body, backed Havana's application in January.
But EU member states are split over the issue.
Spain, a large investor in Cuba, favours granting the country preferential status.
The UK and Sweden oppose it, citing human rights concerns.
The EU recently told Havana it had to improve its human rights situation - a demand cited by the dissident petitioners.
"It is the opinion of those signing this declaration, it is evident that the current Cuban Government has not satisfied a minimum of those proposals," the petition said.
The EU now has its first diplomatic office in Cuba
Signatories included Mr Roca, son of the late Communist leader Blas Roca and formerly Cuba's longest-serving political prisoner; veteran activist Elizardo Sanchez; and dissident economist Marta Beatriz Roque.
The petition was given to the EU development commissioner, Poul Nielson, who was in Cuba to open the EU's first diplomatic office in Havana.