He joins fellow midfielder Kieran Lee and striker Gary Hooper on the sidelines as the Owls head to Wigan Athletic for Saturday's opening-day clash.
The 31-year-old didn't feature in the final pre-season workout, against Spanish side Villarreal last weekend, after pulling up with a hamstring complaint.
"Almen Abdi is injured," said manager Jos Luhukay. " Kieran Lee and Gary Hooper are working intensively to try to get back. They are also not available for Saturday."
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Abdi arrived at Hillsborough in a Â£4 million deal from Watford in Jul 2016 but has managed only 12 league starts for Wednesday.
"It's difficult what has happened with him (Abdi)," Luhukay said. "In the last two years he has has a couple of injuries.
"He trained for four weeks of pre-season. He did every training session and also played minutes in the (early) friendly games we had. He has now been 10 days not training with the team."
The player is being monitored by the Owls' medical team and fitness staff as he takes the first steps towards a comeback. No timeframe has been put on his return.
"We must wait for the reaction from Abdi," Luhukay said. "He's now slowly back in individual training. We have to have some patience before he can start anew with the team."