The 32-year-old winger was forced off after sustaining the injury during South Africa's 29-24 victory at FNB Stadium and has subsequently been ruled out of Saturday's Rugby's Greatest Rivalry series decider against New Zealand in Baltimore.
Kolbe shared a photograph of himself in hospital alongside his wife, Layla, who flew up to be with him following the injury.
The two-time Rugby World Cup winner also thanked fans for their messages of support while sending his best wishes to his Springbok teammates ahead of the clash at M&T Bank Stadium.
"Thank you for all the messages and support. Thank you to my wife for flying up to be here too and doing the most," Kolbe wrote.
"All in God's hands and purpose. Let's go boys!"
Kolbe also gave fans a closer look at the injury, posting a photograph of his broken jaw as he begins his recovery.
The injury is expected to keep him out of action for several weeks, with jaw fractures typically requiring around six to eight weeks before a player can resume contact training. As a result, Kolbe is unlikely to be available for South Africa's one-off Test against Australia in Perth on 26 September.
The Boks' November campaign provides a more realistic target for his return. South Africa begin their Nations Championship campaign against Italy on 7 November, before facing France in Paris on 13 November and Ireland in Dublin on 21 November.
Kolbe's Springbok teammates were quick to send their support, with Ox Nche commenting "Speedy recovery Oompa", while Damian de Allende wrote "love you boeta". Jesse Kriel also responded with a series of heart emojis.
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Springbok No. 8 Jasper Wiese revealed that they are fully focused on their clash with the All Blacks despite the enormity of the occasion in Baltimore.
John Smit believes Malcolm Marx has established himself as the greatest hooker ever to represent the Springboks.
