Potts had replaced Jack Collison just after the hour mark at the Emirates Stadium, but suffered a nasty concussion following a heavy fall after an accidental aerial collision with Bacary Sagna.
The 18-year-old spent Wednesday night in hospital and underwent further scans and tests on Thursday, which came back positively.
Potts has expressed his gratitude for the messages of support he has received and will undergo a period of rest before being allowed to resume light training in the gym.
FIFA president Sepp Blatter had earlier expressed his backing for Potts, writing on Twitter: "Best wishes & quick recovery to @DanPotts03. Concussion in football is a big issue that FIFA is taking very seriously."