We present a kilowatt-level quasi-continuous-wave (QCW) cryogenically cooled 946-nm slab laser oscillator for the first time, to the best of our knowledge. The laser system is based on a double-face-pumped large-size single-slab Nd:YAG design, delivering a record-high average power of 1.06 kW without additional amplification. This laser oscillator operates at repetition rate of 400 Hz with a pulse duration of 175 µs, resulting in a single pulse energy of 2.65 J. To the best of our knowledge, these results represent the highest output power and pulse energy for any all-solid-state 946-nm laser ever reported to date. Our scheme paves a new path for the development of the compact high-power solid-state 946-nm laser.