Abstract We investigate the CO excitation and interstellar medium (ISM) conditions in a cold gas mass-selected sample of 22 star-forming galaxies at z = 0.46–3.60, observed as part of the ALMA Spectroscopic Survey in the Hubble Ultra Deep Field (ASPECS). Combined with Very Large Array follow-up observations, we detect a total of 34 CO transitions with J = 1 up to 8 (and an additional 21 upper limits, up to J = 10) and 6 and transitions (and 12 upper limits). The CO(2–1) and CO(3–2)-selected galaxies, at and 2.5, respectively, exhibit a range in excitation in their mid-J = 4, 5 and high-J = 7, 8 lines, on average lower than ( -brighter) BzK-color- and submillimeter-selected galaxies at similar redshifts. The former implies that a warm ISM component is not necessarily prevalent in gas mass-selected galaxies at . We use stacking and Large Velocity Gradient models to measure and predict the average CO ladders at z < 2 and z ≥ 2, finding and , respectively. From the models, we infer that the galaxies at z ≥ 2 have intrinsically higher excitation than those at z < 2. This fits a picture in which the global excitation is driven by an increase in the star formation rate surface density of galaxies with redshift. We derive a neutral atomic carbon abundance of , comparable to the Milky Way and main-sequence galaxies at similar redshifts, and fairly high densities (≥104 cm−3), consistent with the low-J CO excitation. Our results imply a decrease in the cosmic molecular gas mass density at z ≥ 2 compared to previous ASPECS measurements.