Losing world number one-ranked bowler Steyn on top of Amla, who tops the ICC's batting rankings, would be a huge blow for the Proteas, who need to win in Dubai to claim a share of the two-Test series.
Amla is back in South Africa with his heavily pregnant wife while Steyn has a hamstring strain which will be assessed again on Wednesday.
Proteas team manager Dr Mohammed Moosajee said: "Hashim's wife hasn't given birth yet, so he won't be playing in tomorrow's Test match.
"Dale sustained what was initially thought to be a right hamstring strain but fortunately the MRI scan revealed that there was no major pathology so we are treating it as tightness.
"He will undergo a fitness test either this afternoon or at the latest in the morning.
"The challenge with a tight hamstring is the fear of aggravating it. It could easily become a strain or progress into a tear, so we will be managing it carefully especially with a long tour ahead of us."