A spokesman for the Canadian-owned team had previously said on Thursday that was not the case.
In a video message on Twitter, however, Perez said he had taken a private plane home to see his mother for two days after she suffered an accident.
"As soon as she left hospital. I was able to see her. And then I came back to Europe. Same way, with all the protocols in place. I just got it, I don't know from where. I have no symptoms at all," said the 30-year-old.
Mexico is one of the countries worst hit by the pandemic, with 416,179 total confirmed infections, according to the Health Ministry's latest official count.
The country's death toll as of Thursday was 46,000, almost the same as the United Kingdom which has the third-highest in the world.
"It is one of the saddest days in my career," said Perez, who is now in self-isolation and also likely to miss the following 70th Anniversary Grand Prix at Silverstone.
"The amount of preparation that we put into this weekend, to be 100% ready for it. I knew I had a great car underneath me and the team have done a fantastic job.
"I'm really sad that this happened, but this just shows just how vulnerable we are all to this virus," added Perez, who is sixth in the championship with Racing Point challenging for third.
Perez is being replaced this weekend by Nico Hulkenberg, who raced for the team when it was Force India, leaving them last year.
“I don’t think Checo did anything wrong going back to his family, he takes all the precautions. I think it’s no different to Ferrari going back to Italy, for example,” said Racing Point team principal Otmar Szafnauer.
“We’ve got no clauses in the contract where he’s got to ask for permission to go back to his family. I think his family was in Mexico and it’s not a surprise that he went back to Mexico, that’s what he’s done forever while he’s been driving for us.
"We did though discuss how he was flying there and back. It was always via private flight so never commercially. So there’s no issue with that.
“He’s OK, we’re going to check on him daily, send a doctor to him – he’s quarantining now – and we just have to make sure the virus gets out of his system and he comes back racing.”