The anti-corruption prosecutor said it was basing its appeal on the principle of "equality before the law", implying that the duchess was being unfairly treated because of her royal rank.
"The imputation against a person of facts that, a priori, do not have criminal characteristics supposes at the least a discriminatory treatment," said the written appeal by the prosecutor.
On Wednesday, Judge Jose Castro in Palma on the Mediterranean island of Mallorca summoned the 47-year-old duchess to testify as a suspect on April 27 in a case targeting her husband.
The anti-corruption prosecutor asked the judge to suspend the hearing until the provincial court had a chance to rule on its appeal.
A spokesman for the royal palace had expressed "surprise" over the judge's decision to summon Cristina, after declining to name her as a suspect in March 2012.
The royal family was in "complete agreement" with the prosecutor's decision to appeal the decision, he said when the summons was announced.
The case, which was opened at the end of 2011, is centred on allegations of embezzlement and influence peddling against Cristina's husband, former Olympic handball player Iñaki Urdangarin, and his former business partner Diego Torres.
The pair are suspected of overbilling regional governments to stage sports and tourism events, and then syphoning off money to the non-profit Noos Institute, which Urdangarin chaired from 2004 to 2006.
The Infanta Cristina — seventh in line to the Spanish throne — had seemed set to avoid being snared by the case.
But the judge said evidence, including emails provided to the court by her husband's former business partner, raised doubts that she really was unaware of the business operations of Noos.
Closing the case without hearing the duchess, who was a member of the Noos board, would "discredit the maxim that justice is equal for all", he said.
The duchess, who works as the director of social welfare programmes for the charitable foundation of Barcelona-based financial services group La Caixa, is accused of cooperating by allowing the lustre of her royalty to be used by Noos.