Shaw's head bounced off the ground after his clash against Spain's Dani Carvajal and he had to be stretchered out in an oxygen mask after the horrific injury.
Shaw was fantastic for United in the first 4 matches of the Premier League 2018-19 campaign.
Shaw later tweeted on Saturday evening: "Thank you for all the love and support I am doing fine and am in the best hands".
Gareth Southgate announced that Luke Shaw was okay despite what seemed like a horrifying injury, and since then Mata has responded with a blog post on his website, entitled "Get well soon, Luke".
But Southgate expects him to be back soon and is confident that after the mandatory time off concussion sufferers must take, he will be straight back in training.
US southeast braces for 'days and days' of floods from hurricane
Isaac became a tropical storm again approaching the Caribbean, while Hurricane Helene was veering northward, no threat to land. ET (0900 GMT), according to the NHC, which warned it would be "an extremely unsafe major hurricane" through Thursday night.
The left-back scored his first goal for the club in their 2-1 victory against Leicester and was named United's player of the month for August.
Shaw's absence comes as a huge blow to the defender, who had started the season in impressive fashion for United.
Marcus Rashford score for England while Saul Niguez and Rodrigo secured victory for the Spanish side.
The pair could make their senior bows on home turf this Tuesday as the King Power Stadium plays host to the Three Lions' friendly against Switzerland.
Shaw was nowhere to be seen as the United players arrived for training yesterday, but the defender was photographed driving himself to Carrington at 9.30am today.