We introduce TurBLiMP, the first Turkish benchmark of linguistic minimal pairs, designed to evaluate the linguistic abilities of monolingual and multilingual language models (LMs).Covering 16 linguistic phenomena with 1000 minimal pairs each, TurBLiMP fills an important gap in linguistic evaluation resources for Turkish.In designing the benchmark, we give extra attention to two properties of Turkish that remain understudied in current syntactic evaluations of LMs, namely word order flexibility and subordination through morphological processes.Our experiments on a wide range of LMs and a newly collected set of human acceptability judgments reveal that even cutting-edge Large LMs still struggle with grammatical phenomena that are not challenging for humans, and may also exhibit different sensitivities to word order and morphological complexity compared to humans.