The photo, taken by proud father Prince Carl Philip, shows the fifth-in-line to the throne sound asleep in a bassinet covered in blankets while dressed in a white sleeper suit.
Prince Carl Philip took the photo of his newborn son.
The baby's name was announced earlier this week, with Carl Philip's father King Carl XVI Gustaf revealing his grandson's name and title at a cabinet meeting, according to Swedish royal tradition.
Prince Alexander Erik Hubertus Bertil, Duke of Sodermanland, was born at 6:25 pm at the Danderyd hospital in Stockholm and weighed about 7 pounds 9 ounces. A statement on the royal Facebook page said: "The Marshal of the Realm is delighted to announce that HRH Princess Sofia gave birth to a healthy child."
The new parents are already back at home at Drottningholm Palace, and officials have stated that the family of three are "doing well," following the birth and that the Prince and Princess are "looking forward" to spending time with their son.
The couple looked glowing with happiness in their first photo with their baby son.
The couple have already shared one photo of their family, smiling as they held their son's car seat with little Alexander fast asleep.
Prince Carl was seen attending a special thanksgiving service with his family on Friday and seemed to be coping well with the sleepless nights thus far, looking his usual handsome self in a smart suit and silver tie.
Prince Alexander is the second child to be born to the Swedish royal family this year, as Crown Princess Victoria welcomed her second child Prince Oscar in March.