The princess, distant cousin of King Felipe VI, was 86 years old and died in Paris on March 26, her brother said.
His funeral was held in Madrid on Friday.
France recorded a total of 40,174 confirmed cases of the virus on Sunday, according to the French public health website. Those are 2,599 more cases than on Saturday, marking an increase of 6.9%, a smaller increase than in recent days.
Spain has also registered a smaller percentage increase in the number of cases in recent days. The country has recorded more than 80,000 cases and 6,803 deaths, according to figures from Johns Hopkins University.
The British royal family has also been affected by the global pandemic.
Prince Charles, first in line to the British throne, tested positive for coronavirus on March 25. Carlos, 71, was in isolation for seven days.