MADRID — Spain’s Supreme Court upheld a prison sentence on Tuesday for Iñaki Urdangarin, the brother-in-law of King Felipe VI, in a fraud case that rocked the monarchy and could send a member of the country’s royal family to prison for the first time in modern history.

The court ruled that Mr. Urdangarin must serve five years and 10 months, five months less than the sentence imposed last year by a regional court on the island of Majorca.

The lower court had found Princess Cristina, Mr. Urdangarin’s wife and the king’s sister, not guilty of criminal charges, but fined her about $312,000 for her involvement in her husband’s businesses. On Tuesday, the Supreme Court cut that amount in half.

The case dates to 2011, when an investigation was begun into Mr. Urdangarin’s business activities, which mostly involved organizing sports events for regional governments. The probe was initially prompted by huge cost overruns for the construction of a cycling track on Majorca.