Swedish Soldiers on Skeppsholmen island in Stockholm as well as military stations in Boden, Härnösand, Karlskrona and Gothenburg paid tribute to the latest addition to the royal family, with 21 shots fired from each location.
In Stockholm the celebrations took place as the sun shone on the capital, with temperatures hovering around 15C.
Madeleine gave birth to the baby boy on Monday afternoon, just two days after her brother Prince Carl Philip married Sofia Hellqvist in a busy week for the royal family.
“I am tired but very happy,” her British-born American businessman husband Chris O'Neill told reporters on Tuesday morning. The dad-of-two smiled and gave a thumbs-up as he left Danderyd Hospital north of Stockholm just before 8am.
Sweden's King Carl XVI Gustaf has also been photographed visiting the new prince in hospital.
Sweden's King at Danderyd Hospital on Monday. Photo: TT
The parents are set to officially name their son, who is sixth in line to the Swedish throne, on Thursday, before parliament takes its summer break.
According to Sweden's Aftonbladet, Eugen is the most popular name being betted on at Swedish bookmakers, with Oscar, Wilhelm and Paul also popular.
But the tabloid suggests its readers would like to see the new prince called Zlatan (after Sweden's top goal scorer in history, Zlatan Ibrahimovic).
However Swedish historian and author Herman Lindqvist told the newspaper:
“I think the chance is very small. I do not think Chris O'Neill knows who Zlatan is, he probably thinks it's a drink.”
The couple's first child, Princess Leonore, was born in New York in 2014.