Rico suffered "a serious mishap due to a mule cart and a horse that hit him", his family said in a statement late on Sunday. Spanish paper Marca reported that Rico had been riding a horse himself.
The Spaniard was given permission by PSG to take part in the pilgrimage.
"Sergio is in good hands, fighting to recover while receiving the best care from the medical team at the Virgen del Rocio Hospital. We must exercise caution, especially during the next 48 hours," his family said.
"We are now awaiting medical results, which we hope will be positive, so that we can inform you of his improvement as soon as possible," they added.
Every spring, hundreds of thousands of devotees converge on a shrine to pay homage to the Virgin of the Rocio in an event that combines religious fervour and festive colour in Andalusia.
Rico joined PSG in 2020 after a season-long loan at the capital club. He started his career with Spanish club Sevilla.
