Peperomia asterophylla is a species of epiphyte in the genus Peperomia that is endemic in Peru. It grows on wet tropical biomes. Its conservation status is Threatened.
The type specimen were collected near Santa Rosa, Peru at an altitude of .
Peperomia asterophylla is a medium-sized, stoloniferous herb with a suberect, tufted growth habit. Its stems are 2 to 3 mm thick and velvety at the nodes. The leaves are arranged in whorls of three to five at each node, elliptical in shape with a bluntly pointed tip and an acute base. They measure in length and in width, with three obscure nerves. When dried, the leaves are dull and minutely wrinkled, smooth or nearly so. The petioles are 3 to 4 mm long and brown-velvety. The flower spikes are axillary and terminal, 40 to 80 mm long and 2 mm thick, borne on a nearly smooth peduncle long. The floral bracts are rounded and peltate.
It was described in 1936 by William Trelease in ', from specimens collected by Ellsworth Paine Killip & Dorothea Eliza Smith. It got its name from the description of the type specimen.
It is endemic in Peru. It grows on a epiphyte environment and is a herb. It grows on wet tropical biomes.
This species is assessed as Threatened, in a preliminary report.