The 18-year-old landed awkwardly and was briefly knocked out after a clash with Bacary Sagna during the second half of his side's 5-1 defeat.
He lay motionless on the Emirates turf for 10 minutes as medical staff attended to him and was given oxygen before being carried off on a stretcher and in a neck brace.
West Ham confirmed the defender would be receiving more attention to aid his recovery.
A statement on the club's official Twitter feed read: "West Ham United can confirm that Dan Potts will undergo scans and further assessment in hospital on Thursday.
"On behalf of Dan, the club would like to thank fans for all their messages of support for the defender and join them in wishing him well."
Speaking after the match, manager Sam Allardyce said: "Potts was unable to give the correct answers to the questions the doctor asked, which shows a concussion to the brain.
"They put him on the oxygen and strapped him, just to make sure there was no damage to the spine or the neck.
"He was out for a few seconds, maybe a minute, and was not fully conscious when he came off.
"We were concerned at how long it took. They have to make sure they protect the spine the right way, getting them on the stretcher - that is why it took the time it did.
"Hopefully he will make a speedy recovery. As he lost consciousness it is a minimum of two weeks, I think, before he can play again."
FIFA president Sepp Blatter has expressed 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."