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."
Irons boss Sam Allardyce stressed on Wednesday that the utmost care had to be taken because of the nature of the injury.
Speaking after the match, 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."