We present the physical extent of C ii 158 m line-emitting gas from 46 star-forming galaxies at z = 4-6 from the ALMA Large Program to INvestigate C ii at Early Times (ALPINE). Using exponential profile fits, we measure the effective radius of the C ii line ( ) for individual galaxies and compare them with the rest-frame ultraviolet (UV) continuum ( ) from Hubble Space Telescope images. The effective radius exceeds by factors of ∼2-3, and the ratio of increases as a function of Mstar. We do not find strong evidence that the C ii line, rest-frame UV, and far-infrared (FIR) continuum are always displaced over 1 kpc scale from each other. We identify 30% of isolated ALPINE sources as having an extended C ii component over 10 kpc scales detected at 4.1 -10.9 beyond the size of rest-frame UV and FIR continuum. One object has tentative rotating features up to ∼10 kpc, where the 3D model fit shows the rotating C ii-gas disk spread over 4 times larger than the rest-frame UV-emitting region. Galaxies with the extended C ii line structure have high star formation rate, high stellar mass (Mstar), low Ly equivalent width, and more blueshifted (redshifted) rest-frame UV metal absorption (Ly line), as compared to galaxies without such extended C ii structures. Although we cannot rule out the possibility that a selection bias toward luminous objects may be responsible for such trends, the star-formation-driven outflow also explains all these trends. Deeper observations are essential to test whether the extended C ii line structures are ubiquitous to high-z star-forming galaxies.