Salah scored directly from a corner in his side’s 4-1 victory, but went down injured clutching his left leg. He received treatment and was substituted as a result.
Speaking after the match, Egypt assistant coach Hany Ramzy played down the seriousness of the injury.
“The initial diagnosis, according to the team doctor, is a strong muscle strain. It is not a tear, I think it is not serious,” said Ramzy.
After scoring 44 goals in all competitions during his first season at Anfield, the striker has netted only three this term, with just one since August.
Salah netted twice and missed two penalties when record seven-time African champions Egypt hammered Niger 6-0 last month in another qualifier.
With eSwatini ranked even lower than Niger, there were expectations that Salah could get back on the goal trail at the Al Salam Stadium in the Egyptian capital.
He blasted a shot wide with Egypt three goals ahead before curling a corner into the net on the stroke of halftime.
Salah fluffed a chance to net again by missing from inside the box during the second half after combining with Arsenal midfielder Mohamed Elneny.
Captain Ahmed Elmohamady, Amr Warda and Mahmoud Hassan also scored for Egypt and Sibonginkosi Gamedze snatched a late eSwatini consolation goal.
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