Abstract We use the Cosmic Assembly Deep Near-infrared Extragalactic Legacy Survey data to study the relationship between quenching and the stellar mass surface density within the central radius of 1 kpc (Σ 1 ) of low-mass galaxies (stellar mass M * ≲ 10 9.5 M ⊙ ) at 0.5 ≤ z < 1.5. Our sample is mass complete down to ∼10 9 M ⊙ at 0.5 ≤ z < 1.0. We compare the mean Σ 1 of star-forming galaxies (SFGs) and quenched galaxies (QGs) at the same redshift and M * . We find that low-mass QGs have a higher Σ 1 than low-mass SFGs, similar to galaxies above 10 10 M ⊙ . The difference of Σ 1 between QGs and SFGs increases slightly with M * at M * ≲ 10 10 M ⊙ and decreases with M * at M * ≳ 10 10 M ⊙ . The turnover mass is consistent with the mass where quenching mechanisms transition from internal to environmental quenching. At 0.5 ≤ z < 1.0, we find that Σ 1 of galaxies increases by about 0.25 dex in the green valley (i.e., the transition region from star forming to fully quenched), regardless of their M * . Using the observed specific star formation rate gradient in the literature as a constraint, we estimate that the quenching timescale (i.e., time spent in the transition) of low-mass galaxies is a few (∼4) Gyr at 0.5 ≤ z < 1.0. The mechanisms responsible for quenching need to gradually quench star formation in an outside-in way, i.e., preferentially ceasing star formation in outskirts of galaxies while maintaining their central star formation to increase Σ 1 . An interesting and intriguing result is the similarity of the growth of Σ 1 in the green valley between low-mass and massive galaxies, which suggests that the role of internal processes in quenching low-mass galaxies is a question worthy of further investigation.