The centre-back has been a key part of the Swiss side that have shone in Germany so far, holding the hosts to a draw in the group stages before knocking out holders Italy with ease in the last 16.
England, by contrast, have stumbled their way into the last eight. The Three Lions needed a stoppage-time equaliser from Jude Bellingham, before beating Slovakia 2-1 after extra-time in the last 16.
"No matter how they have played, they are in the quarter-finals," said Schar. "They can hurt their opponents at any time so we need to be prepared for that.
"I wouldn't underestimate England. They have seen us play in the last few games, they know what our strengths are, but for Switzerland it would be great to show what we are capable of."
England boss Gareth Southgate is reportedly considering a switch to a back three in order to address his side's issues and match up to Switzerland's 3-4-3.
Swiss boss Murat Yakin said he was more focused on his own side and matching their displays against Germany and Italy.
"We don't know what England plans to do but they have a lot of quality in their team," said Yakin.
"We are in good shape, we have a lot of self-confidence and we have shown in several games we can play against big teams.
"We played well against the defending champions, against the hosts, so we will cause problems for England and we will see what happens in the end."
Switzerland had suffered an injury scare earlier in the week when Granit Xhaka had a scan on a muscle problem.
However, the influential midfielder, who played a huge role in Bayer Leverkusen's unbeaten league and cup double in Germany last season, has been passed fit to play.
"Granit has a lot of experience, he is fit and he trained with the team," added Yakin. "I count on him 100 percent and think he will play a great game tomorrow with the team."
