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4 year oldProsecutors say they were given the false documents when they landed in the capital Asuncion on Wednesday.
The pair had been taken in for questioning and their hotel was searched by police.
They deny wrongdoing and say they thought the passports were a courtesy gesture.
In July 2019, the player reportedly had his Brazilian and Spanish passports confiscated over unpaid taxes and non-payment of fines for illegally building on a nature reserve in Brazil.
"I respect his sporting popularity but the law must also be respected. No matter who you are, the law still applies", Mr Acevedo told local media earlier this week.
The 39-year-old had travelled to Paraguay to promote a book and a campaign for underprivileged children.
Ronaldinho was the 2004 and 2005 World Player of the Year and reached the prime of his career at Spanish giants Barcelona. He won the World Cup for Brazil in 2002 alongside fellow superstar forwards Ronaldo and Rivaldo.
Ronaldinho's net worth is estimated at £80-100m and he is reported to charge around £150,000 for a single promoted Instagram post.
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