Aims. Whereas the evolution of gas kinematics of massive galaxies is now relatively well established up to redshift z similar to 3, little is known about the kinematics of lower mass (M-* \textless= 10(10) M-circle dot) galaxies. We use MUSE, a powerful wide-field, optical integral-field spectrograph (IFS) recently mounted on the VLT, to characterize this galaxy population at intermediate redshift. Methods. We made use of the deepest MUSE observations performed so far on the Hubble Deep Field South (HDFS). This data cube, resulting from 27 h of integration time, covers a one arcmin(2) field of view at an unprecedented depth (with a 1 sigma emission-line surface brightness limit of 1 x 10(19) erg s(-1) cm(-2) arcsec(-2)) and a final spatial resolution of approximate to 0.7 `'. We identified a sample of 28 resolved emission-line galaxies, extending over an area that is at least twice the seeing disk, spread over a redshift interval of 0.2 \textless z \textless 1.4. More than half of the galaxies are at z similar to 0.3 similar to 0.7, which is a redshift range poorly studied so far with IFS kinematics. We used the public HST images and multiband photometry over the HDFS to constrain the stellar mass and star formation rate (SFR) of the galaxies and to perform a morphological analysis using GALFIT, providing estimates of the disk inclination, disk scale length, and position angle of the major axis. We derived the resolved ionized gas properties of these galaxies from the MUSE data and model the disk (both in 2D and in 3D with GALPAK(3D)) to retrieve their intrinsic gas kinematics, including the maximum rotation velocity and velocity dispersion. Results. We build a sample of resolved emission-line galaxies of much lower stellar mass and SFR (by similar to 1-2 orders of magnitude) than previous IFS surveys. The gas kinematics of most of the spatially resolved MUSE-HDFS galaxies is consistent with disk-like rotation, but about 20% have velocity dispersions that are larger than the rotation velocities and 30% are part of a close pair and/or show clear signs of recent gravitational interactions. These fractions are similar to what has been found in previous IFS surveys of more massive galaxies, indicating that the dynamical state of the ionized gas and the level of gravitational interactions of star-forming galaxies is not a strong function of their stellar mass. In the high-mass regime, the MUSE-HDFS galaxies follow the Tully-Fisher relation defined from previous IFS surveys in a similar redshift range. This scaling relation also extends to lower masses/velocities but with a higher dispersion. We find that 90% of the MUSE-HDFS galaxies with stellar masses below 10(9.5) M-circle dot have settled gas disks. The MUSE-HDFS galaxies follow the scaling relations defined in the local Universe between the specific angular momentum and stellar mass. However, we find that intermediate-redshift, star-forming galaxies fill a continuum transition from the spiral to elliptical local scaling relations, according to the dynamical state (i.e., rotation-or dispersion-dominated) of the gas. This indicates that some galaxies may lose their angular momentum and become dispersion-dominated prior to becoming passive.