Captain America: The First Avenger stuck closely to the comic books by pitting Steve Rogers against the Red Skull in his first World War II-set adventure. In the movie, we learned that Johann Schmidt had been left with that hideous appearance after taking HYDRA's version of the Super-Soldier Serum, but Marvel Studios explored another possible origin story for the character at one point.
As you can see, concept artist Ryan Meinerding has shared an early take on the Red Skull which reveals that using the power of the Tesseract is what would have led to his startling transformation.
Ultimately, Marvel Studios took things in a different direction and made it so that no one could really hold the Tesseract (unless they were particularly powerful beings like Loki and Thanos). This definitely would have been a cool idea to explore on screen, though, and fans remain optimistic that the villain will be brought back to the Marvel Cinematic Universe in the not too distant future following his surprise return in Avengers: Infinity War.
Check out this Captain America: The First Avenger concept art below: