The trips—which are cleared under existing U.S. Treasury rules that allow approved travelers to go to the island for cultural and humanitarian exchanges—still need a green light from Cuban authorities.
"We look forward to working with the Cuban authorities for their approval to help make the social, cultural and humanitarian exchanges between U.S. citizens and the people of Cuba a reality," Carnival CEO Arnold Donald said in a statement.
It was not immediately clear what additional Cuban approvals the company would need to launch the Miami-to-Cuba trips.
Carnival's efforts come as Washington and Havana attempt to normalize diplomatic relations that were severed more than 50 years ago. The countries last week announced an agreement to re-open embassies in each other's capitals, possibly this month.
The Obama administration has pushed for goods and people to flow more freely between the U.S. and Cuba. The Carnival initiative falls under "fathom," the "social impact" line the carrier launched in June.
Seven-day trips to Cuba would start at $2,990 per person, the company said.
— CNBC's Ryan Ruggiero contributed to this report