Toffees boss Roberto Martinez has revealed that the South African is suffering from a "grade one soft tissue problem", although Arouna Kone seems more likely to feature soon
The South African picked up the injury in the week leading up to Everton's 1-0 win over Chelsea and failed to prove himself sufficiently fit to take a place on the bench.
There was positive news for the Everton boss, however, with Arouna Kone's chances of regaining fitness appearing greater than that of his team-mate.
Martinez told Everton's official website: "I think Steven Pienaar is going to be a little bit longer - it's a grade one soft tissue problem. But Arouna Kone shouldn't be too long."
With injuries forcing Martinez to shuffle his team early in the season, the Spaniard underlined the importance of having strong squad depth.
"It's not about who's missing, it's about who's going to be on the pitch," he continued.
"Creating that competition is going to be vital for us to be competitive across the season and I couldn't be happier that we had two influential players missing [against Chelsea] and we had other players come in and perform and give their all for the team."