The
type specimen were collected near
Huancabamba, Peru.
Peperomia glabrirhachis is a moderately small,
stoloniferous, tufted herb. The stem is 1–2 mm thick, angled, and sparsely covered with retrorse hairs. The
leaves are in whorls of about 4 at the nodes. They are somewhat rhombic-elliptic to obovate, obtuse, with an acute base, measuring 10 mm long and 5–6 mm wide. The leaves are
1-nerved, revolute, sparsely pubescent beneath, and have a papillose-rugose texture on both surfaces. The
petiole is barely 1 mm long. The terminal
spikes are 15 mm long and 1 mm thick, glabrous, and borne on a filiform, velvety
peduncle about as long as the spike itself. The floral
bracts are round-peltate. ==Taxonomy and naming==