The Force India duo have clashed in both Canada and Azerbaijan this season in a car that has shown that it could be capable of a podium finish.
But, Ocon has been bombarded with insulting messages for his part in the closely-fought battle and has been left with no option but to take action.
“I blocked them because they insulted my parents, and that is not healthy,” said Ocon.
“It’s just a sport. We fight hard, but we’re not murderers. So people need to calm down.”
Ocon also said he is not worried about stepping on Perez’s home patch later this year at the Mexican Grand Prix.
“I think everything will be fine,” he added.
“I never said anything bad about Mexico. I like the country, I had a great time there in the past and I have a good relationship with Sergio.”