The City boss is believed to have flown out of the country this morning and assistant manager Brian Kidd takes charge of the team for Thursday's friendly with Amazulu.
Pellegrini is not expected to return before City head to Hong Kong on Sunday, but the club are hopeful he will be back for next week's Barclays Premier League Asia trophy.
City will face South China on Wednesday before taking on either Sunderland or Tottenham next Saturday.
The former Malaga boss has only been in charge of training since July 8th after being named as the successor to Roberto Mancini.
City have continued their summer spending in the absence of Pellegrini as Fiorentina confirmed they have agreed a deal with the club for striker Stevan Jovetic.