Steenkamp has made 53 international appearances for the Springboks and was part of the 2007 World Cup-winning squad.
The 36-year-old loosehead prop will fill in for his compatriot Heinke van der Merwe.
"He will be able to train today (Monday) and will be available for the first match of the Top 14 at home to Lyon on Saturday," Stade Francais said in a statement.
Steenkamp, who has made 53 international appearances for the Springboks and was part of the 2007 World Cup-winning squad, previously played six seasons for Toulouse before leaving earlier this year.
Elsewhere in the Top 14, Toulon flanker Charles Ollivon has been ruled out for three to four months with a shoulder injury he suffered in a pre-season friendly against Lyon last Thursday, club president Mourad Boudjellal said.
The 24-year-old, who has played six times for France since making his international debut in 2014, joins full-back Jonah Placid on the sidelines, leaving last season's runners-up Toulon looking for medical jokers before their season-opener against Pau on Sunday.