We present a certified defense to clean-label poisoning attacks under $\ell_2$-norm. These attacks work by injecting a small number of poisoning samples (e.g., 1%) that contain bounded adversarial perturbations into the training data to induce a targeted misclassification of a test-time input. Inspired by the adversarial robustness achieved by $randomized$ $smoothing$, we show how an off-the-shelf diffusion denoising model can sanitize the tampered training data. We extensively test our defense against seven clean-label poisoning attacks in both $\ell_2$ and $\ell_{\infty}$-norms and reduce their attack success to 0-16% with only a negligible drop in the test accuracy. We compare our defense with existing countermeasures against clean-label poisoning, showing that the defense reduces the attack success the most and offers the best model utility. Our results highlight the need for future work on developing stronger clean-label attacks and using our certified yet practical defense as a strong baseline to evaluate these attacks.