Liverpool get their season underway on Sunday, 16 August against Tottenham at White Hart Lane, a match which Skrtel is now doubtful for.
The Slovakia international featured 30 times for Liverpool last season and his absence would be a major blow to manager Rafael Benitez.
El Zhar has only started four games since arriving at Anfield from French side St Etienne in 2006 but Benitez recently handed the Moroccan a new deal to tie him to the club until 2012.
Midfielder Steven Gerrard, who missed the Reds' Far East pre-season tour in order to attend a court case, will not join up with the club for the Singapore game despite being found not guilty of affray.
"We were in touch with him every day and knew what was happening and we were confident everything would be okay," said Benitez.
"Now we need to take care of him, he must rest.
"I have to protect my players. We have already lost two to injury, Martin Skrtel and Nabil El Zhar."
Fans in Asia had been disappointed at missing out on seeing Gerrard whose image was used prominently in promotional material to sell tickets.
"I'm sorry for the fans that we can't bring Gerrard but he is the captain of the team so he is a key player for the rest of the season," added Benitez.
"I hope the fans can respect the decision. We have other big names like Pepe Reina, Xabi Alonso, Fernando Torres and Javier Mascherano and they are all here."
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