The American screamed in agony after slipping during the third set against Romania's Sorana Cirstea on court 17.
The Women's Tennis Association (WTA) said more will be known following Friday's tests.
"Bethanie of course thanks everyone for their kind wishes and messages of support," the WTA statement added.
"She is resting tonight but wants to chat tomorrow [Saturday] via Facebook Live so she can let everyone know how she's doing and answer some questions."
Mattek-Sands was treated by paramedics on the court before being carried off on a stretcher and taken straight to hospital.
The 32-year-old later wrote on social media: "To the best family, friends and fans a girl could ask for, it's been a painful and emotional 36 hours but thank you for all the love and support."
Mattek-Sands had been favourite to add a Wimbledon doubles title to her US Open, Australian Open and French Open victories with Czech partner Lucie Safarova, who went to the court when she heard about the injury.
Mattek-Sands has also received support from the tennis world. Nine-time Wimbledon singles champion Martina Navratilova wrote on social media: "Am just devastated about Bethanie Mattek-Sands and her injury - we are all behind you, hoping for the best - lots of love, m."
American Wimbledon singles champion Chris Evert added: "Going over the day and remembering @BMATTEK [Bethanie Mattek-Sands] in my thoughts and prayers and wishing this very special lady a speedy recovery..."
Andrew Castle, BBC Sport tennis commentator:
The club monitor the moisture levels of the grass at all times but when it's hot, it wilts and dies and then can become slippery.
I spoke to the Centre Court groundsman who told me his plan. This morning, he put the roof over and soaked it to give it a drink and a rest. We all need that every now and again.
The trouble is the players aren't used to it as they don't play on it for much of the year - they are mostly on clay or hard courts.
Hopefully they understand it's a natural surface and it does show natural signs of wear and tear.
Bethanie Mattek-Sands is having more scans on a serious knee injury she picked up during her second-round Wimbledon singles match on Thursday.