He suffered the injury in a game against Wingate & Finchley, which was halted after the incident.
Vigar was placed in a medically induced coma and underwent surgery in an attempt to aid his recovery, but unfortunately, his injuries were too severe.
Chichester City Football Club has released a statement confirming Vigar's passing and expressing their condolences to his family.
The club has asked that the family's privacy be respected during this difficult time.
A statement from the club reads: "After sustaining a significant brain injury on Saturday, Billy Vigar was placed in an induced coma and underwent surgery to aid any chances of recovery.
Unfortunately, despite the operation, the injury was too severe, and Vigar passed away on Thursday morning.
The club has received an outpouring of support from the football community, showing the love and appreciation for Vigar within the sport.
Vigar's family is deeply saddened by his passing, as it occurred while he was doing the thing he loved – playing football.