The goalkeeper received a severe head injury after falling from a horse in the Spanish village of El Rocio, Spanish news website Mucho Deporte reported, citing sources.
It added that Rico had been immediately sent to a hospital in Sevilla and placed in an intensive care unit.
The COPE broadcaster specified that the horse that Rico was riding became nervous when a horse-drawn carriage ran into it. The goalkeeper fell and the animal kicked him on the head. In addition to a head injury, he suffered a brain hemorrhage, the report said.
On Saturday, Rico's club won the 11th Ligue 1 title with a draw against RC Strasbourg Alsace. The goalkeeper, who was on the bench for that game, traveled to Spain later as he was given some time off by the club, The Daily Mirrior reported.
Rico, 29, joined PSG in the 2019-2020 season and has played 24 games for the club, winning two Ligue 1 titles. Before coming to PSG, he played for Spain's Sevilla, Mallorca and England's Fulham.