Zwikker was born in Zaandam as the son of Klaartje Dil and the shopkeeper Klaas Cornelisz Zwikker. He married Johanna Dorothea Theinert (*1901, Zaandam) in 1924 in Zaandam. In 1918 he had started studying chemistry and later physics at the University of Amsterdam, where in 1925 he obtained his PhD with the thesis "Physical properties of wolfram at high temperatures" under supervision of the Noble-laureate Pieter Zeeman. From 1923 he worked as scientific researcher at Philips in Eindhoven, but in 1929 he was appointed professor in theoretical and applied physics at the Delft University of Technology. He was involved in the acoustic design of sound studios and presided over multiple physics-related organizations. In 1945 he requested retirement from his professoriate in Delft and became technical director of the "light" section at Philips. Between 1956 and 1970 he again was professor of physics, now at the Eindhoven University of Technology. He lived in Eindhoven until the death of his wife in March 1984 and died in Zwijndrecht in 1985.
Zwikker is the author of the classic geometry textbook, The Advanced Geometry of Plane Curves and Their Applications, designed to teach the applications of complex numbers to the study of curves and to the resolution of problems in geometry and engineering.
Zwikker wrote many books; the best known are the following:
- Sound Absorbing Materials (1949, with C. W. Kosten)
- The Advanced Geometry of Plane Curves and Their Applications (1963)
- Biography by H. K. Nagtegaal. (in Dutch)
- C. Zwikker, 1900 - 1985 at the University of Amsterdam Album Academicum.
- de Faubert Maunder, M. J. "An improved field test for barbiturates and hydantoins with a modified cobalt(II) thiocyanate reagent". The Analyst. 100 (1197). doi:10.1039/an9750000878.
- David Havelock; Sonoko Kuwano; Michael Vorländer (Editores) (2008). Handbook of Signal Processing in Acoustics. Springer Science & Business Media. p. 1169. ISBN 978-0-387-77698-9.
- Rida T. Farouki (2008). Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable. Springer Science & Business Media. p. 48. ISBN 978-3-540-73397-3.
- H. K. Nagtegaal. Genealogische en Historische Encyclopedie van Delft, deel II (1988), blz. 247, 248. (in Dutch)
- H. K. Nagtegaal. 60 jaar studie voor natuurkundig ingenieur te Delft, blz. 98. (in Dutch)