High-silica (gel Si/Al = 100) SSZ-13 membranes were prepared by hydrothermal secondary growth on the surface of α-alumina hollow fiber supports. The membranes were evaluated for their performance in the separation of CO2 from equimolar mixtures with CH4 or N2. The maximum CO2–CH4 and CO2–N2 separation selectivities were found to be 42 and 12 respectively, with a high CO2 permeance of 3.0 × 10−7 mol m2 s−1 Pa−1 at 293 K and total feed pressure of 0.6 MPa. At the low aluminum content, the prepared membranes contain a very low number of defects, as follows from their H2/SF6 ideal selectivity of over 500 in the 293–473 K temperature range. Due to their hydrophobicity, water in the feed mixture has only a small influence on the permeance at temperatures above 353 K. Water improves the CO2–N2 and CO2–CH4 selectivity, which is attributed to preferential blocking of the hydrophilic, non-zeolitic defect pores. The hydrothermal stability of the high-silica SSZ-13 membrane was evaluated by a long (220 h) CO2–N2 separation test with a humidified (9.5 kPa H2O) feed mixture at 393 K and 0.6 MPa feed pressure. The permeance and selectivity were stable during this endurance test, underpinning the promise of high-silica SSZ-13 membranes for application in the separation of hot and humid gas mixtures.