The online editions of Spain's leading daily newspapers El Pais and El Mundo featured the low-quality video of Princess Cristina from behind as she answered a judge's questions on Saturday.
The video, lasting five minutes and 23 seconds, was posted on a video-sharing website, wouzee, by a user identified only as "infanta" (princess). The leaked video is the only content posted under that user name.
Judge Jose Castro had banned recordings at the closed-door hearing in his court in Palma de Mallorca, prohibiting anyone from entering the courtroom with a camera or telephone that could record images.
Today, the video itself was posted online and picked up by the press, prompting condemnation by the chief judge of the Balearic islands, Francisco Martinez Espinosa.
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"It is being investigated and if the person is found who did it they should pay the legal consequences," Espinosa told reporters.
Cristina, 48, is at the centre of a scandal over alleged fraudulent business dealings by her husband, former Olympic handball player Inaki Urdangarin.
She was grilled for over six hours on Saturday over allegations she was complicit in tax-dodging and money laundering.