We report on single-pass high-harmonic generation (HHG) with amplified driving laser pulses at a repetition rate of 20.8 MHz. An Yb:YAG Innoslab amplifier system provides 35 fs pulses with 20 W average power at 1030 nm after external pulse compression. Following tight focusing into a xenon gas jet, we observe the generation of high-harmonic radiation of up to the seventeenth order. Our results show that state-of-the-art amplifier systems have become a promising alternative to cavity-assisted HHG for applications that require high repetition rates, such as frequency comb spectroscopy in the extreme UV.