Rain saw the entire morning session ruled out, with the toss delayed by three-and-a-half hours. Bar a couple of senior players and management, the England team did not even leave their hotel until 75 minutes after the game was due to begin.
When they arrived at the Wanderers, Archer — who has bowled at good pace over the past couple of days — was unable to prove his fitness.
Archer, who misses his third-straight match with the injury, looked distraught as the team learnt the news.
Mark Wood, who returned to the side in Port Elizabeth but has been sore early in the week, was passed fit to play in a side set to show one change.
Chris Woakes was set to come into an all-seam attack in place of the off-spinner Dom Bess, who took a maiden Test five-wicket haul last week.
England lead the series 2-1 with one match to play.