As optical and near-infrared surveys stare deeper into the Universe, galaxy clusters continue to be discovered at ever larger distances, allowing us to observe the growth of structure over cosmic time. When we observe the light from these clusters, or count the galaxies they contain, we do not get a full measure of their mass, since they are dominated by dark matter. The gravitational deflection of light from background sources (‘gravitational lensing’) does let us weigh the total gravitating matter content of galaxy clusters, and several studies have measured the distorted shapes of background galaxies for this purpose, but for very distant clusters, background galaxies become difficult to find and measure precisely in galaxy surveys. On the other hand, the Cosmic Microwave Background (CMB) can serve as a background light source for clusters at much larger distances. In this work, we use CMB lensing to measure the mass of the most distant blindly-selected sample of galaxy clusters to date. In CMB data from the the Atacama Cosmology Telescope (ACT) and the Planck satellite, we detect the stacked lensing effect from 677 near-infrared-selected galaxy clusters from the Massive and Distant Clusters of WISE Survey (MaDCoWS), which have a mean redshift of 〈z〉 = 1.08 (when the Universe was 5.6 billion years old, compared to its present age of 13.7 billion years). There are no current optical weak lensing measurements of clusters that match the distance and average mass of this sample. We detect the lensing signal with a significance of 4.2 sigma. We model the signal with a halo model framework to find the mean mass of the population from which these clusters are drawn. Assuming that the clusters follow Navarro-Frenk-White density profiles, we infer a mean mass of 〈M500c〉 = (1.7 +- 0.4) × 1014 Msun. This work highlights the potential of CMB lensing to enable cosmological constraints from the abundance of distant clusters populating ever larger volumes of the observable universe, beyond the capabilities of optical weak lensing measurements.