Mobbie suffered a fractured eye socket following a clash of heads early in Bafana's 3-0 Group C victory over Lesotho on Friday. The Sekhukhune United defender was stretchered off and underwent surgery on Saturday morning.
"The injury happened as a result of a clash of heads in the first half and he sustained a fracture of the eye socket in three places," Bafana's team doctor Tshepo Molobi told Safa.net.
Monyane, who joined Chiefs this season after leaving Orlando Pirates, is expected to join Hugo Broos' squad in Bloemfontein this weekend.
There was further relief for Bafana as Stellenbosch FC defender Thabo Moloisane, who also went off with a head injury against Lesotho, was cleared to return to training on Saturday.
South Africa sit five points clear at the top of Group C. Victory over Nigeria at the Free State Stadium would take them a step closer to qualification for the 2026 World Cup.