Monger remains in a critical, but stable condition.
At the time of writing more than 12,000 people had donated in excess of £500,000 ($640,000).
Among the scores of donors were 2009 F1 world champion Button who donated £15,000 ($19,000) as well as posting on his Instagram account urging people to give money.
“This guy needs our help so if you can please donate, I will be doing as much as I can to help this dude out…” Button wrote.
Mercedes driver and three-time F1 world champion Lewis Hamilton also lent his support.
“Thoughts and prayers are with you and your family, @BillyMonger,” Hamilton tweeted Wednesday.
Red Bull Racing’s Verstappen donated £5,000 with the message: “My thoughts go out to you and your loved ones. Stay strong Billy!”
Monger’s cousin Vicky posted a message on her Facebook account thanking well-wishers for the outpouring of support.
The series was launched in 2014 as a way of bridging the gap between karting and the Formula 3 European Championship.