Navidi sustained a grade two hamstring tear in the gripping 20-19 quarter-final win over France.
Bongi Mbonambi has credited coach Rassie Erasmus for the Springboks' turnaround in performances.
The 40-year-old will be thrown straight into his coaching duties when the Port Elizabeth side takes on the Cape Cobras in the 4-Day Series on Monday.
City are the bookmakers' favourites to finally win the biggest prize in European football after more than a decade of huge investment from the club's Abu Dhabi owners and in Guardiola's fourth season in charge.
South Africa progressed into a World Cup semifinal against Wales after a 26-3 victory over Japan on Sunday.
France led 19-10 when Sebastien Vahaamahina was sent off in the 49th minute in Tokyo for elbowing Aaron Wainwright on Sunday. Wales won 20-19.
A surprise league defeat by newly-promoted Real Mallorca on Saturday has put the pressure back on Zinedine Zidane, who led Madrid to three consecutive Champions League triumphs in his first spell in charge at the club.
Chris Silverwood was hired as Trevor Bayliss' successor earlier this month and will lead England for the first time on their forthcoming tour of New Zealand.
The tourists will bat again trailing by 335 runs in response to India's 497 for nine declared in Ranchi.
Kaizer Chiefs are through to quarterfinals after edging City 4-2 on penalties after the two sides players to a 1-1 all draw after 120 minutes of play.
