We present the physical extent of [C ii] 158µm line-emitting gas from 46 star-forming galaxies at z = 4−6 from the ALMA Large Program to INvestigate CII at Early Times (ALPINE). Using exponential profile fits, we measure the effective radius of the [C ii] line (r e, [CII] ) for individual galaxies and compare them with the rest-frame ultra-violet (UV) continuum (r e,UV ) from Hubble Space Telescope images. The effective radius r e, [CII] almost always exceeds r e,UV by factors of ∼ 2-3 and the ratio of r e,[CII] /r e,UV increases as a function of M star . We do not find strong evidence for a displacement over 1-kpc scale among the [C ii] line, the rest-frame UV, and FIR continuum. We identify 30% of isolated ALPINE sources as having an extended [C ii] component over 10-kpc scales detected at 4.1σ-10.9σ beyond the size of rest-frame UV and far-infrared (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 (SFR), stellar mass (M star ), low Lyα equivalent-width, and more blue-shifted (red-shifted) rest-frame UV metal absorption (Lyα line), as compared to galaxies without such extended [C ii] structures. Although we cannot rule out the possibility that a selection bias towards luminous objects may be responsible for such trends, the extended [C ii] line structure appears even around several objects whose SFR and M star are as small as those without the extended structure. Deeper observations are essential to test whether the extended [C ii] line structures are ubiquitous to high-z star-forming galaxies.