Senderos limped out of the game in the 36th minute before the Swiss completed the biggest upset of the tournament with a 1-0 win over the European champions.
"We know that Philippe will miss the next two games but he will stay with the team," Von Ah said.
"He had an X-ray in Johannesburg today and it showed that there are no broken bones, just a painful distortion of his ankle," he added.
Von Ah said the centre back, who last week moved to Fulham from Arsenal, had been downcast fearing the worst.
"He is feeling much better; he was really down last night, but the pictures from the X-ray proved to be encouraging," Von Ah said.
The Swiss team is also nursing striker Alex Frei and midfielder Valon Behrami, recovering from ankle and thigh injuries respectively.
Von Ah said Behrami took part in full training with the team on Thursday, while Frei is still undergoing a special training programme.
Switzerland play Chile in their second Group H match on Monday in Port Elizabeth, before taking on Honduras in the final group match in Bloemfontein on June 25.
