The IOC has told at least one athlete, Australian snowboarder Tora Bright, to refrain from using a sticker.
"For us it is a question of what is appropriate," IOC spokesman Mark Adams told reporters. "We have huge sympathy and she (Burke) needs to be well remembered either individually or collectively.
"The competitions themselves are not the right place to do that and we would like to keep that separate."
He said the IOC could help organise another event or news conference to remember multiple X Games champion Burke, who died in January from injuries sustained in a training crash in Park city, Utah.
She had successfully lobbied for the inclusion of the superpipe event at this year's Sochi Games.
"I ride with a Sarah sticker on my snowboard and helmet always. The IOC however, consider Sarah stickers 'a political statement' and have banned them. WOW," Bright wrote on social networking site Instagram.
"Sarah is a beautiful, talented, powerful woman, who's spirit inspires me still. She is a big reason why skier pipe/slope are now Olympic events."
The IOC also sent a letter to the Norwegian Olympic Committee reminding them that their decision to wear black armbands in memory of an athlete's relative who had died before the start of the Olympics in Russia was inappropriate.
The brother of cross-country skier Astrid Uhrenholdt Jacobsen died suddenly a day before the Games opened and the wanted to commemorate him and support their athlete.
Norway's four skiers in Saturday's skiathlon raced with black armbands in memory of Jacobsen's brother.
IOC officials said the letter to the NOC was not an official reprimand but rather a reminder of the rules.
(Editing by Peter Rutherford)
