Quantum signatures of a free electron in interaction with a continuous-wave radiation field are investigated by looking for negativities in the Wigner function of the system. The free-electron wave function in the radiation field is calculated fully analytically by solving the appropriate Schr\"odinger equation in the Krammers-Henneberger frame. It is found that pronounced quantum signatures show up already for a laser peak field of magnitude ${E}_{0}=1\text{--}2\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ and a frequency $\ensuremath{\omega}=1\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ However, the nonclassical behavior gets lost if the interaction with the radiation field is taken in the dipole approximation.