The Swiss qualified for their first major tournament quarter-final since 1954 with a stunning win on penalties over reigning world champions France in Bucharest on Monday.
Neither trained Wednesday with Belgium's medical staff working around the clock to get them fit to face Italy.
There had been concern about the extent of the injuries after both players had to be replaced in the second half of Belgium's 1-0 victory over Portugal on Sunday in the round of 16.
Eden Hazard said that he will stay with the Belgium squad until the end of Euro 2020 even if a hamstring injury rules him out of the tournament.
Hazard has been hampered by injuries ever since making the move from Chelsea to Real Madrid.
Axel Witsel will also play from the start in the game in St.Petersburg in Monday as Martinez looks to give three of his most important and experienced players some extra game time.
With Eden Hazard also recovering from injury, his brother Thorgan took the initiative for Belgium, scoring with his shin in the 20th minute off a cross from Yannick Carrasco.
On paper, at least, because the form of some of the players on the top-ranked FIFA team raises a big question mark on its ability to go deep at this year's European Championship.
Hazard has struggled to contribute since joining Real for a reported 100 million euros ($122 million) from Chelsea in 2019.
Sergio Ramos will be back in the squad after recovering from an injury that has kept him out since March.
Belgium team for Euro Cup: Eden Hazard, Romelu Lukaku, Kevin De Bruyne all included by Roberto Martinez
Martinez also selected a group of 11 reserve players who could step up in case of injuries ahead of the tournament, which opens on June 11.
Hazard counts it as a blessing to make it through a single match without another muscle creaking let alone an entire season worthy of international acclaim.
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Januzaj's superb second-half goal sent Belgium into a last 16 clash with Japan while England will now advance to a second round meeting with Colombia.
England impressed in their opening two World Cup games, but in Belgium they face the world's third-ranked side, and a squad loaded with world-class talent such as Eden Hazard and Kevin De Bruyne.