The alleged incident occurred in the second half of the Springboks’ 21-10 victory over the Scots at Murrayfield on Saturday.
Etzebeth, 21, will appear before an International Rugby Board disciplinary hearing today.
The IRB’s recommended sanctions for any player found guilty of eye-gouging range from a low entry point of 12 weeks to a high entry point of 24 weeks with a maximum possible ban of three years.
South Africa, who beat Ireland the week before they travelled to Edinburgh to face the Scots, play England at Twickenham on Saturday.
Argentina prop Juan Figallo, meanwhile, has been cited for head-butting France captain Pascal Pape at the end of the Pumas’ 39-22 defeat in Lille on Saturday night.
Figallo’s hearing is listed for tomorrow. Argentina face Ireland in Dublin on Saturday in another autumn Test.