Burger was cited by New Zealand's Stephen Hinds for an act "contrary to good sportsmanship by allegedly attacking the eyes of Luke Fitzgerald". His punishment matches that handed down to Italian skipper Sergio Parisse at the weekend for a similar offence in the game against New Zealand.
The ban means Burger will not only miss the third Test agianst the Lions in Johannesburg this weekend, but also South Africa's opening three matches in the 2009 Tri Nations Series - two games against New Zealand in Bloemfontein and Durban and the first clash with Australia in Cape Town on 8 August.
He will be eligible to play again in the world champions' fourth round match in the tournament against Australia in Perth on 29 August. The ban imposed by Canadian judicial officer Alan Hudson was the second of a lengthy day of proceedings in Pretoria.
Earlier in the day Mr Hudson found Bakkies Botha guilty of a dangerous charge on Adam Jones, which left the Welshman with a dislocated shoulder. The two hearings took 12 hours to complete.
The Lions camp roundly criticised Burger for his actions and he could have been given an even longer sentence. The prescribed minimum entry point for eye gouging in the IRB Disciplinary Code is 12 weeks - the length of ban that original Lions pick Alan Quinlan received for his gouging offence in the Heineken Cup semi-final.