The little prince was held in the arms of his mother Sofia and seemed to be fast asleep as he was oblivious to the hubbub from both the crowd and the Navy Band, which was performing Abba songs.
In the prince's first public photograph he was also slumbering.
“This place is special for us. It was where we announced our engagement, and received warm cheers after our wedding,” said Sofia as she welcomed the crowds to the palace grounds and gardens.
Many visitors took advantage of the sunny weather to visit the castle and there were very long queues, according to Swedish newspaper Expressen.
Carl Philip, 36, is the second child and only son of King Carl XVI Gustaf and Queen Silvia of Sweden. His elder sister Princess Victoria is first in line to the throne.
Prince Alexander already has plenty of royal cousins to play with. Prince Oscar, the second child of Princess Victoria, was born just seven weeks ago. He is the younger brother of four-year-old Princess Estelle.
London-based Princess Madeleine also has two children, Princess Leonore and Prince Nicolas.