The brand, Hawkers, had said on its Mexican Twitter account (@HawkersMX) on Wednesday: "Mexicans, put on these sunglasses so your swollen eyes can't be seen during tomorrow's building of the wall."
U.S. President-elect Trump had promised while campaigning ahead of Tuesday's election to build a "big, beautiful, powerful" border wall with Mexico to stop the flow of undocumented immigrants.
"What a bad commentary. Today I am ending my relations with @HawkerMX," Perez said on his own Twitter account in reply. "I will never let anyone laugh at my country."
Hawkers subsequently said it had made a "serious error," and removed the offending tweet, which it said had not been made in "mockery."
"It will not happen again," the Spain-based company added.
But the tweet also proved to be a deal breaker for the Diablos Rojos of the Mexican Baseball League. The team on Thursday said its players would no longer use the sunglasses, nor would the company's products be sold in its official store.
"We see it as an aggression against Mexico," said Carlos Alberto Fernandez, a spokesperson for the Diablos.
"For the moment, Hawkers is not an option," he said, adding that the team was evaluating other brands.
For his part, Perez, who drives for Force India, would not say how much the brand was paying him, but told reporters at the Brazilian Grand Prix on Thursday that his mind was made up, even though production had started on a run of some 20,000 glasses bearing his name.
The sponsorship deal had only recently been agreed, he added.
"I decided to split with the brand," said the driver, who found out about the comment after landing in Sao Paulo and seeing a lot of angry messages from his fans on Twitter.
"It was a very unfortunate comment about my country .. I didn't find it funny at all. I feel sorry because it's a great brand, they've done really well but I'm not willing to stay there," he added.
"The relationship was going to be very successful but my country and my people come first," added Perez. "I won't let anyone make fun of my country and it's a shame that the brand pays for it because it's a mistake from one person."
(Reporting by Alan Baldwin and Natalie Schachar; editing by Pritha Sarkar and G Crosse)
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