The actions of the 26-year-old Frenchman enraged Liverpool fans with complaints over his behaviour flooding in on internet message boards.
Itandje was instructed by Liverpool manager Rafael Benitez not to attend training on Friday.
A Liverpool spokesperson said in a statement: "Charles Itandje has now been officially suspended for 14 days by the club while we investigate his conduct during the Hillsborough Memorial Service."
The memorial service, attended by players past and present and thousands of Liverpool fans, was to honour the 96 people who died at the FA Cup semi-final clash between Liverpool and Nottingham Forest on April 15, 1989.