The hit single has been played 4.6 billion times across all streaming services, overtaking Justin Bieber's "Sorry", which previously held the title.
The track is currently No. 1 in the US, UK and Australia.
"Streaming is a connector for audiences worldwide and it has helped my music reach every corner of the planet. It is truly an honour that 'Despacito' is now the most streamed song in history," Fonsi said.
"Despacito", which means slowly in Spanish, was released on January 13.
It's also the fastest ever music video to 2 billion views (154 days).