The study by the state polling institute CIS showed that the score for public confidence in the royals fell to 3.68 points out of ten, from 4.97 in October 2011. In November 2010 it had been 5.36.
The question on the royals had not been included in the monthly CIS survey since October 2011, just before Juan Carlos's son-in-law Inaki Urdangarin was named in a corruption probe - the first major public scandal to hit the traditionally popular king's family.
The latest poll was carried out between April 1st and 8th, coinciding with the news that Urdangarin's wife, the king's younger daughter Cristina, was also formally named as a suspect in the affair. She has appealed the summons to go before a judge in the investigation.
The case centres on allegations of embezzlement against Urdangarin and his former business partner when the duke ran a non-profit institution from 2004 to 2006.
Another poll carried out before Cristina's summons and published in El Pais newspaper on April 7th showed that more than half of Spaniards disapproved of the king against 42 percent who approved.
Juan Carlos won wide respect in Spain for helping guide it through a political transition after the death of dictator Francisco Franco in 1975.
But his image suffered last year due to the corruption scandal and an expensive elephant-hunting holiday which he took in Botswana while Spain was struggling through a recession.
Backing for Juan Carlos has declined most sharply among the generation of young Spaniards born after the restoration of the monarchy, the survey in El Pais by pollster Metroscopia showed.
The scandals raised speculation that Juan Carlos would abdicate to make way for his son Felipe, but the king has indicated in recent months that he wishes to continue ruling.