Joachim Low's side came back from the brink in its previous outing against Sweden, ultimately winning 2-1 after falling behind in the first half.
A defeat would have sent Germany packing, but Toni Kroos's sumptuous late strike saw it move level on three points with Sweden.
Given the world champion's troubles so far, a loss to South Korea is by no means out of the question, with Werner and Marco Reus well aware of the threats posed by their Asian counterparts.
"They have a lot of pace – especially up front," Reus said. "They have versatile players who have caused problems for teams at this tournament already."
Werner added: "They have very quick players, Sweden were more about power and size, whereas South Korea are smaller but pacey.
"Son is up there with the best in the world, we have to keep an eye on him. We shouldn't be looking at our opponents too much, though."
Jerome Boateng's late red card for two bookable offences in 11 minutes means Low will be forced into at least one change, with Bayern Munich's Mats Hummels likely to come back into the starting XI after a neck injury.
He may even be partnered with club team-mate Niklas Sule, given Antonio Rudiger's shaky performance against Sweden.
As for South Korea, its unenviable task has been made even more difficult by the news midfielder Ki Sung-yueng will miss out with a calf injury which rules him out for two weeks.
"A medical inspection at a hospital showed that Ki damaged his left calf muscle," a Korean Football Association (KFA) official told Yonhap News. "He needs two weeks of treatment."
If Germany is to ultimately be eliminated from the competition after this match, it would be the third successive reigning champion to not get out of the group stage.