Shikabanegatana

Tsutsuki Tsuranuki, a middle school boy who lives a happy life despite slightly strange family circumstances. But when a great disaster strikes, strange zombie-like creatures kidnap his younger sister. To find the whereabouts of his younger sister, Tsutsuki heads to monster-infested Tokyo, and there has a chance encounter with a high school girl wielding a mysterious sword.

(Source: Kadokawa, translated)