The poll published in centre-left newspaper El Pais showed 53 percent disapproved of the way the 75-year-old head of state is carrying out his functions, against 42 percent who approved.
That gave him an overall approval-versus-disapproval rating of -11, compared to +21 in December, a lower rating than the one received by tax inspectors or lawyers and the first time that he has received a negative rating.
Disapproval of the monarch, who is recovering from surgery in March for slipped discs, his seventh operation in three years, was highest among left-wing voters and people aged 18 to 34.
Among those in this age group, the king's approval-versus-disapproval rating stood at -41.
The poll was carried out by the Metroscopia polling firm for the newspaper in March, before a judge on Wednesday named the king's youngest daughter, the Infanta Cristina, as a suspect in a corruption case.
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 Inaki 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 king 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 steep recession and a record jobless rate of 26 percent.
The king broke his hip during the trip and had to be flown home for medical care.
He issued an unprecedented public apology after his return but the affair fuelled calls from some quarters that he should abdicate in favour of his 45-year-old-son, Prince Felipe, the youngest of his three children with Queen Sofia.
The hunting trip — reportedly subsidized and organized by Syrian construction magnate Mohamed Eyad Kayali — threw the spotlight on the royal family's deluxe lifestyle and opaque fortune.
It also drew attention to the king's friendship with Corrina Sayn-Wittgenstein, a blonde German aristocrat who is 28 years his junior, after it emerged that she accompanied him on the trip to Botswana.
Felipe's approval ratings have also taken a hit but remain broadly favourable.
A majority of Spaniards, 61 percent, approve of Felipe against 33 percent who disapprove, giving him an overall approval-versus-disapproval rating of +28, compared to +37 in December.
The poll also showed general dissatisfaction with political institutions, with the corruption allegations affecting the royal family just one in a series of scandals hurting Spain's political and economic elite.
Fully 93 percent of those polled said they disapproved of the way politicians carried out their role, 91 percent were disapproving of political parties and 90 percent said they disapproved of the behaviour of banks.
If a general election was held now, the ruling centre-right Popular Party would capture just 24.5 percent of the vote while the main opposition Socialist Party would get 23 percent, a separate poll published in El Pais showed.
The Popular Party won 44.6 percent of the vote in a landslide election win in November 2011.
But the party has been rocked by allegations that top members, including Prime Minister Mariano Rajoy, for years received under-the-table payments on top of their official salaries.