The German led from start to finish as Mercedes secured their first win since re-entering the sport three years ago.
That performance has led Button to confess that the Brackley-based outfit, for whom he won a world championship while they were under the ownership of Brawn GP, will rival his McLaren team and Red Bull for this year's constructors title.
"I spent a lot of years with that team - most of my career was with that team - so I am very happy for them they've achieved a grand prix victory this year," Button told the Press Association.
"There's a great bunch of people there, and people that went back to the team as well that I used to work with, like Geoff Willis, so that does obviously pose a threat to us in the championship."
Meanwhile, security concerns continue to hover over this weekend's race in Bahrain after four Force India team members were caught in a petrol bomb attack.