British F4 officials say Monger is in a "critical, but stable condition," having had both legs amputated while in an induced coma.
"Due to the injuries sustained and despite every effort, Billy has sadly had both lower legs amputated," they said in a statement.
"He has been kept in an induced coma while undergoing surgery, from which he is expected to be woken in the next few days."
Monger's family is seeking donations to fund the "care, treatments and therapies" the teenager now requires "to return to a full and active life."
By this morning, the total had reached £302,000 ($548,000) after it began with a £260,000 target.
"Having always been a fighter Billy has already overcome big hurdles in his career," the family said on the fundraising website JustGiving, which described the incident as "one of the most horrific crashes Motorsport has seen."
"Struggling for budget Billy has fought his way into top-flight motorsport, however, we now need your kindness and support to help give Billy and his family the best chance to fight these injuries that will affect Billy's life so massively."