"We continue to thank everyone for their loving warmth and well wishes regarding our marriage," the princess wrote in English, six days after marrying US-British finance executive Christopher O'Neill.
"Sadly, the Swedish tabloid press have taken it upon themselves to destroy our privacy and place private photographs of us in their publications today," she added.
"The one thing we wish is that, if only for these few days, our privacy can now be respected."
The couple had decided to stay at the same hotel as Prince William and Kate Middleton did during their honeymoon, according to the tabloid.