De Bruyne asked to be substituted because of an injury after being tackled from behind by Portugal's João Palhinha earlier in the game. He slowly walked off the field with a slight limp.
De Bruyne sat down pointing to his left ankle and shook his head. He seemed fine after he first picked up the injury during the first half, but he couldn't continue after only two minutes into the second half.
Dries Mertens entered the match in De Bruyne's place.
Belgium's injury issues then worsened minutes from full-time when Hazard was taken off with an apparent hamstring injury after pulling out of a challenge and asking for a sub on the near touchline.
"We will take 48 hours now to assess the situation of the two players. We go back to Belgium now and they will have scans on the injuries tomorrow," Belgium boss Roberto Martinez said at his post-match news conference.
"It's too early to say how they are doing. With Kevin, it's the ankle -- he couldn't really turn in the second half. With Eden it's the muscle, but we have to wait for a diagnosis."
Both players were injured before the start of the tournament but had recovered well to help Belgium finish top of their group and remain vital to the team's hopes of advancing at Euro 2020.
Belgium will next play Italy in the quarterfinals on Friday, July 2.