The 18-year-old, who had a loan spell at Colchester earlier this season, fell to the ground after jumping in a challenge with Gunners defender Bacary Sagna with 18 minutes left.
It appeared the youngster, on as a substitute, hit his head on the pitch, and was momentarily knocked out.
Potts received lengthy treatment from medical staff, eventually being taken from the field on a stretcher, in a neck brace, receiving gas and covered in an emergency blanket before being transferred to a nearby hospital for observation.
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."