Pienaar made a shock decision in October to quit playing for Bafana Bafana, just three months before the Africa Cup of Nations, and the national team has been rocked by the loss of its captain and playmaker.
The 30-year-old admitted he was struggling to cope with the physical demands of combining his club career with international fixtures and Igesund was unable to convince Pienaar to make a U-turn.
Igesund, who met with Pienaar in England last month, said he is "totally retired from international football" and will "get on with his life at his club."
Pienaar, who is having his second spell at Goodison Park, has been a key player for the Toffees this season as they have made a strong start to the Premier League campaign.
South Africa will prepare for the tournament with friendlies against Malawi, Norway and Algeria before their opening match against debutant Cape Verde on 19 January.