The weird usage seems to have developed in the same way as "a headquarters". Consider the following Ngram:
The original phrase seems to have been "shambles" or "the shambles", almost always plural. It meant "a place for slaughtering animals", but later came to be also used for scenes of carnage, scenes of great disorder, and certain dangerous shoals at sea.
Etymonline says that "shambles" originally meant "meat market", having evolved from the word schamil meaning "table or stall for vending". I assume that it naturally started out as a plural, because there would be several butcher's stalls at a meat market.
However, once "shambles" came to mean "a scene of great disorder or carnage", the things it referred to were more naturally singular, and so "shambles" slowly came to be used as a singular.