Castro made the offer late on Sunday as he criticised American policies toward his country during a three-hour appearance on state television and announced a protest march for Tuesday outside the American embassy in Havana.
Because travel to Cuba by most Americans is prohibited under US sanctions, Castro asked US authorities to give Americans official permission to travel to Cuba for the operations.
"We're ready to send an airplane to Florida to pick them up," Castro said. Cuba would foot the costs of flights, accommodation and the surgery, Castro said.
Cuba has all the equipment and specialised personnel considered among the best specialists in the world, he said. He asked if the US government would prohibit those people from travelling to the island and "sentence them to blindness".
However, political relations between America and Cuba are worsening so American approval to let its citizens travel - even for health reasons - appeared unlikely.
Cuba teamed up with Venezuela in recent months for a free eye surgery programme that brings impoverished people from around the region to the island for free treatment.
Venezuela, meanwhile, recently expanded its programme to provide subsidised heating oil to poor Americans.