In a 1000km orbit, you'll need a mirror about 9km across to appear 0.5° in diameter from the ground (the same size as the Sun), and therefore light up an area with the same illumination as the Sun.
Note that you can't make due with a smaller mirror focused to a tighter area, as the brightest thing the mirror can reflect is the Sun, and so it must appear at least as large as the Sun in the sky to illuminate any point on the ground by the same amount.
With the much dimmer goal of moonlight illumination levels, the mirror shrinks to 9km / sqrt(400,000) = 14.2m in diameter, which is actually rather reasonable. However it would only illuminate an area 0.5° wide from the mirror's point of view, or around 9km. And because the mirror is orbiting at 7.4km/s, you'd only get a second or two of illumination.
TLDR: Moonlight mirror 14m across, could light up a 9km diameter area for a little over a second.
Edit: In the case of a permanent mirror in geostationary orbit, a 500m mirror could provide moonlight illumination to an area around 300km in diameter.