On Monday, the club said: “Billy received a significant brain injury and is currently in an induced coma in intensive care receiving the best possible treatment.
“It is too early to say what the outcome will be and even if things go well, there will be a long road to recovery.”
Vigar is a graduate of the Arsenal academy and has also had spells at Derby County, Hastings and Eastbourne Borough.
Posting on social media, Arsenal expressed their hopes for Vigar’s “speedy recovery”.
“Everyone at Arsenal sends love and support to Billy and his loved ones at this difficult time.” they said.
Chichester said the game against Lewes will be rescheduled at a later date.