Background Cannabis use and cannabis use disorder (CUD) is increased in patients with schizophrenia. It is important to establish if this is explained by non-causal factors, such as shared genetic vulnerability. We aimed to investigate whether the polygenic risk scores (PRS) for schizophrenia and other psychiatric disorders would predict CUD in controls, patients with schizophrenia, and patients with other psychiatric disorders. Methods We linked nationwide Danish registers and genetic information obtained from dried neonatal bloodspots in an observational analysis. We included people with schizophrenia, other psychiatric disorders, and controls. The exposures of interest were the PRS for schizophrenia, attention-deficit hyperactivity disorder (ADHD) autism spectrum disorder, and anorexia nervosa. The main outcome of interest was the diagnosis of CUD. Results The study included 88 637 individuals. PRS for schizophrenia did not predict CUD in controls [hazard ratio (HR) = 1.16, 95% CI 0.95-1.43 per standard-deviation increase in PRS, or HR = 1.47, 95% CI 0.72-3.00 comparing highest v. remaining decile], but PRS for ADHD did (HR = 1.27, 95% CI 1.08-1.50 per standard-deviation increase, or HR = 2.02, 95% CI 1.27-3.22 for the highest decile of PRS). Among cases with schizophrenia, the PRS for schizophrenia was associated with CUD. While CUD was a strong predictor of schizophrenia (HR = 4.91, 95% CI 4.36-5.53), the inclusion of various PRS did not appreciably alter this association. Conclusion The PRS for schizophrenia was not associated with CUD in controls or patients with other psychiatric disorders than schizophrenia. This speaks against the hypothesis that shared genetic vulnerability would explain the association between cannabis and schizophrenia.