Jedinak, captain for club and country, started the second-round tie at home to Shrewsbury Town but was forced off early in the second half.
Speaking after his team's 4-1 extra-time victory over the League One outfit, Eagles manager Alan Pardew expressed his concerns about the holding midfield player.
"I'm a little bit worried about the skipper, he might have done a hamstring, but we'll have to wait and see," Pardew said.
"We think he might have done something a little bit long term, but we'll have to assess him in the morning."
Any fitness problem would come as a blow to the 31-year-old, who has found himself out of the Palace first team early in the Premier League season following the arrival of France international Yohan Cabaye from Paris Saint-Germain.
Australia coach Ange Postecoglou will face a nervous wait to learn the extent of Jedinak's injury as he prepares for the Socceroos' FIFA 2018 Russia World Cup Qualifier™ at home to Bangladesh and away to Tajikistan on September 3 and 8 respectively.