The Toffees boss says several members of his squad have been hit by a bug which is proving "nearly impossible to control".
Bryan Oviedo, who was taken to hospital on Wednesday with a chest infection and is now a major doubt for the FA Cup quarter-final clash with Chelsea this weekend, is the fourth player to be hit by the bug in recent weeks.
Tom Cleverley has been missing for the club's last two matches after being struck down by illness, whilst Gareth Barry was fit enough only for the bench in the defeat to West Ham, and Arouna Kone missed the FA Cup win over Bournemouth last month.
Martinez revealed that he and his staff are struggling to control the bug which appears to be sweeping the club's training ground and admitted that it is a serious concern at a crucial point in Everton's season.
The Spanish boss said, as quoted by the Echo: "It’s nearly impossible to control. The doctors are looking into the infection but there is not a clear source. It has been a real concern for us.
"For Tom Cleverley, to drop out as he did and lose so much weight was a concern, but it affects different players in different ways. Gareth Barry didn’t lose any weight but found it very difficult to be able to breathe. Bryan Oviedo has a chest infection but it hasn’t affected his nutrition.
"The problem is, there is no sign of the chest infection. It usually happens overnight... it is not something you can see building up and feel as though it is going to come."
Fortunately for the Toffees, Cleverley and Barry appear to have recovered enough from the illness to be back in contention to face Chelsea on Saturday, but Oviedo is unlikely to be fit.
Everton are looking to reinvigorate their season by booking a place at Wembley with victory over the Premier League champions at Goodison Park.