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This paper proposes a stretchable-substrate-impregnated fabric for deployable high-gain antenna for small satellites. Constellations of small satellites offer worldwide coverage of wireless communication and earth observation; high-gain antennas are required to realize high-speed communication and high-resolution radar. This paper aims to develop a CubeSat onboard high-gain reflectarray antenna that can be folded compactly and deployed in space. The novelty of this paper is the stretchable-substrate-impregnated fabric, which can realize low stowage volume with high fabrication tolerance and low resistivity with single-piece reflectarray to avoid gain degradation. The origami-folding-pattern compatible reflection elements can avoid creases on the elements, avoiding gain reduction after folding. A $17\times 17$ -element reflectarray using the stretchable-substrate-impregnated fabric and the origami-folding-pattern compatible reflection elements is designed, fabricated, and characterized. The folded volume of the reflectarray is 27 mm in height and 58 mm in diameter, and the measured fabrication tolerance of the reflection element was $20 ~\mu \text{m}$ at most. Electrical antenna measurements confirmed low resistivity of 1.20 $\text{m}\Omega /\Box $ and a high realized gain of 23.6 dBi, comparable with conventional flexible printed circuit reflectarray antennas. The simulated and measured antenna efficiency is 25.3% and 25.1%, respectively. The simulated and measured 1-dB gain down bandwidth is 1.6% and 1.5%, respectively.