The discussion of senior leaders' private lives is extremely rare in China, and the exact birth dates of most of them are not revealed publicly, as they are considered a state secret.
State television showed pictures of Xi and Putin at the hotel he is staying at in Dushanbe, the capital of Tajikistan, where they are both attending a regional summit, Presstv Reported.
While Putin gave Xi Russian ice cream - the flavor was not mentioned - Xi gave Putin back some Chinese tea, the report said.
Xi thanked Putin and said that in China Putin was extremely popular, it added.
Pictures on Chinese state television's website showed the two men inspecting a white cake decorated with red and blue confectionery flowers with the words written on it, in somewhat shaky red-colored Chinese characters, "good fortune double six".
It was not immediately clear if Xi ate any of the cake.