De Bruyne was forced off early in the second half during his side's 1-0 win over Portugal on Monday (AEST), a result that saw the reigning European champion knocked out at the last-16 stage.
The Manchester City midfielder was seen with ice on his left ankle while watching on from the sideline, where he was later joined by Hazard after the Real Madrid winger damaged his hamstring late in proceedings.
Martinez is preparing to be without the pair when the Red Devils take on the Azzurri in Munich on Friday, though remains hopeful they can feature if Belgium progress to the last four.
"The initial information that we have from medical staff is positive for both, they will remain with the squad and they have no structural damage," Martinez told the media on Monday.
"But we are up against time and it is very difficult to see them fully fit. We have to take it day by day to try and get them fit.
"We were all a bit concerned before we got the news from the scans and it was a relief to all that we can now work on trying to get them fit again."
Eden's brother Thorgan Hazard scored the only goal of the game against Portugal, sending Belgium through to the last eight for a second successive European Championship.
They lost at the same stage of the previous edition, however, going out to Wales in 2016.