"We'll see how the treatment affects his recovery and we'll have a better idea on Monday or Tuesday next week."
Jagielka suffered a hamstring injury in Saturday's 1-1 Premier league draw at Watford.
Influential midfielder Ross Barkley, who hurt his knee in the same game, is fit for the trip to 16th-placed Palace however.
"Barkley has progressed really well and the knock he had is quite soft and I would expect him to be fit and available for tomorrow," said Martinez.
Midfielder Tom Cleverley was "50/50" for Wednesday but Martinez doubted there would be any long-term problem.
Everton have dropped 16 points from leading positions in the Premier League this campaign, which includes squandering a two goal advantage three times.
Their home form has also been poor, with eight of their 10 league losses coming at Goodison Park, and Everton are now 14th in the table and heading for their lowest finish in more than a decade.
Martinez is under increasing pressure but the Spaniard refused to blame his players, while pointing at areas that needed improvement.
"We haven't been able to manage games well enough, we haven't conserved leads and have thrown really good positions away. We clearly need to get better," he said.
"As a manager you put pressure on yourself, whether there's scrutiny outside or not, it's always been the same," added the Spaniard.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Alan Baldwin)
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