"Climbing is a way to discover a country, a culture," the French daredevil said before completing the feat, his first in Cuba. "This is a strong sign of support for Fidel Castro."
When asked if he would meet Castro while in Havana, Robert said: "I don't know if he'll be calling me this afternoon."
The 86-year-old Castro, who turned over the country's leadership to his brother Raul in 2006 after he fell ill, on Sunday made his first public appearance in three months when he voted in legislative elections.
The hotel, which first opened in 1958 under a different name, served as a temporary headquarters for Castro after his triumphant march into the capital.
Robert started his climb from the fourth floor of the hotel, located in the heart of Havana, and reached the 26th floor just 28 minutes later. The building is 70 meters (230 feet) high.
Police stopped traffic while Robert completed the feat. The roughly 2,000 spectators applauded each time he reached a higher floor.
The 50-year-old Frenchman has climbed more than 100 structures without ropes or other safety equipment, setting a record for "most buildings climbed unassisted" according to Guinness World Records.