TOKYO — Comme des Garçons and Louis Vuitton feted their much-anticipated temporary store here Wednesday night and racked up a fair spate of orders as Japanese fashion editors and local celebrities rushed to get their hands on one of Rei Kawakubo’s custom-designed bags for the French house.

Located in a small faux brick structure in the trendy Aoyama district, the interiors are true to Comme des Garçons’ spare aesthetic, with gray concrete walls and an exposed metal staircase. Steel boxes coated in LV-logo gold flock are mounted on the walls of the lower level. Each box features a slit or compartment designed to hold a specific model of...