Annica Sönnerborg, head of press at the court, says the current unrest in Ukraine is behind the decision, and adds all royal visits are made following advice from the Foreign Ministry.
They have recommended the Crown Princess should not travel to Russia, she says, but did not give any more details.
The Crown Princess had planned to arrive at Sochi on Sunday and stay for two days. No Swedish government ministers were expected to make the trip.
British Prince Edward was also due to attend the games, but was also advised by the British government not to go.
The Swedish King and Queen were at the Winter Olympics in Sochi several weeks ago, before the latest troubles broke out. Sochi lies a few hundred kilometres down the Black Sea coast from Crimea.
The Paralympics Games start on Friday, Sweden has sent a team of 19 athletes.