The Dutch forward is on a short break in Dubai with his family and decided to make a spontaneous visit to meet his idol.
"I've always admired Maradona since I was a young child," said Van Persie. "He is one of the best footballers of all time, and a visit to Dubai would not have been complete without the opportunity to get to meet him face to face."
Maradona, who was very pleased with the surprise visit, was full of praise for the Dutch striker.
"Van Persie is not only a star player but a footballer with a stellar personality that is something that I hold in high respect. His great talent, combined with his humble character, make him a model for all great players to live by," said Maradona.
Van Persie, who brought his wife Bouchra and two children along with him, also had a kickabout with Maradona, even though he was dressed in jeans and smart shoes.
Arsenal face second-tier English side Leeds United tomorrow in the third round of the FA Cup, though it is not known whether Van Persie will be back in England for that game or whether he is being rested by manager Arsene Wenger.