"She's been very good and kind to her mother," Australian-born Mary said of her daughter, who was born Saturday.
Mary cradled the newborn girl, who was wearing a white hat and wrapped in a blanket, as the royal family walked out of the Copenhagen University Hospital.
Mary and Frederik already have an 18-month-old son, Christian, who is second in line to the Danish throne, after his father. Christian met his little sister for the first time Sunday morning.
"He was enthusiastic to see her and showed a little bit of boyish love," Mary said.
Frederik said the couple was very "fortunate and lucky" to have a girl.
The palace banned the use of flash photography for the royal family's departure from the hospital as security kept the crowds of well-wishers and press in line.
Many Danes arrived at the hospital early Monday bearing Danish and Australian flags in hopes of catching a glimpse of the new princess.
The royal family made their way down a red carpet to their waiting motorcade, which was to bring the family back to their home in Fredensborg Castle, 35 kilometers (20 miles) north of Copenhagen. The new princess will be third in line to the throne after her father and older brother.
She has not been named yet and Mary said that for now she is called "lille pige," which means little girl in Danish.
It is tradition for members of the Danish royal family to receive four names. Danish media and royal experts are speculating that the new princess may be named after Queen Margrethe, Frederik's mother; his maternal grandmother, Ingrid, and Mary's mother, Henrietta.
The discovery of the submarine has unveiled a few "inconsistencies." For example, how can one explain the fact that the sub was found where it needed to be searched for from the start?
When on a state visit to Singapore, Russian President Vladimir Putin promised to revisit the discussion of the 1956 Declaration between the USSR and Japan regarding the issue of the peace treaty with Japan
The TurkStream, which runs along the bottom of the Black Sea from Russia's Anapa to Turkey, will consist of two lines, each with a capacity of 15.75 billion cubic meters of gas a year