The A-League champions resume their group stage games in the Qatar hub on Nov. 19 and Redmayne was a notable omission from the 23-man squad released on Monday.
"With my wife heavily pregnant I couldn't risk missing the birth of my first child," Redmayne said.
"If all goes well things may have been OK, however I'm not prepared to risk something unforeseen happening while I'm away.
"I'm grateful to the club for allowing me to support my wife."
"Andrew doesn't want to miss the birth of his first child understandably, so he'll remain home and work on being ready for the new A-League season," Sydney coach Steve Corica said.
"This is a good opportunity for Tom Heward-Belle to show what he can do in these games, which will give us more depth, game time and experience for these young players ahead of the new A-League season."
The Sky Blues have bolstered their squad with the addition of Milos Ninkovic. The star playmaker was left out of their original squad but Adam Le Fondre's move to Mumbai City FC in the Indian Super League has opened up a foreign spot.