Social media companies are under scrutiny for the prevalence of hateful content on their platforms, but there is scarce empirical evidence of the consequences of regulating such content. We study this question in the context of the ``Network Enforcement Act'' (NetzDG) in Germany, which mandates major social media companies to remove hateful posts within 24 hours. Using a difference-in-differences strategy, we find that the law was associated with a statistically significant reduction in toxic posts by far-right social media users. Further, we show that the NetzDG reduced anti-refugee hate crimes in towns with more far-right Facebook users. Together, these findings suggest that online content moderation can curb online hate speech and offline violence.