Abstract Gas-rich minor mergers contribute significantly to the gas reservoir of early-type galaxies (ETGs) at low redshift, yet the star formation efficiency (SFE; the star formation rate divided by the molecular gas mass) appears to be strongly suppressed following some of these events, in contrast to the more well-known merger-driven starbursts. We present observations with the Atacama Large Millimeter/submillimeter Array (ALMA) of six ETGs, which have each recently undergone a gas-rich minor merger, as evidenced by their disturbed stellar morphologies. These galaxies were selected because they exhibit extremely low SFEs. We use the resolving power of ALMA to study the morphology and kinematics of the molecular gas. The majority of our galaxies exhibit spatial and kinematical irregularities, such as detached gas clouds, warps, and other asymmetries. These asymmetries support the interpretation that the suppression of the SFE is caused by dynamical effects stabilizing the gas against gravitational collapse. Through kinematic modelling we derive high velocity dispersions and Toomre Q stability parameters for the gas, but caution that such measurements in edge-on galaxies suffer from degeneracies. We estimate merger ages to be about 100 Myr based on the observed disturbances in the gas distribution. Furthermore, we determine that these galaxies lie, on average, two orders of magnitude below the Kennicutt–Schmidt relation for star-forming galaxies as well as below the relation for relaxed ETGs. We discuss potential dynamical processes responsible for this strong suppression of star formation surface density at fixed molecular gas surface density.