We present a simple fabrication method for the realization of suspended GaAs nanomembranes for cavity quantum optomechanics experiments. GaAs nanomembranes with an area of 1.36 mm by 1.91 mm and a thickness of 160 nm are obtained by using a two-step selective wet-etching technique. The frequency noise spectrum reveals several mechanical modes in the kilohertz regime with mechanical Q-factors up to 2,300,000 at room temperature. The measured mechanical mode profiles agree well with a taut rectangular drumhead model. Our results show that GaAs nanomembranes provide a promising path towards quantum optical control of massive nanomechanical systems.