Möhring was born in Unna, North Rhine-Westphalia, Germany, but grew up in Herne. His father was an Army officer and his mother worked as a teacher. Möhring has a sister and two brothers. After his brother, Wotan Wilke Möhring, became an actor in the early 2000s, Sönke followed him to also become an actor.
Sönke Möhring made his national debut in Stefan Ruzowitzky's Anatomy 2, where August Diehl also appeared, and his international film debut in Quentin Tarantino's film Inglourious Basterds (2009) where he played private Butz and the minor role of Walter Frazer. Since then, he appeared mostly in German TV movies.