Hands, one of the most dynamic parts of our body, suffer from blur due to their active movements. However, previous 3D hand mesh recovery methods have mainly focused on sharp hand images rather than considering blur due to the absence of datasets providing blurry hand images. We first present a novel dataset BlurHand, which contains blurry hand images with 3D groundtruths. The BlurHand is constructed by synthesizing motion blur from sequential sharp hand images, imitating realistic and natural motion blurs. In addition to the new dataset, we propose BlurHandNet, a baseline network for accurate 3D hand mesh recovery from a blurry hand image. Our BlurHandNet unfolds a blurry input image to a 3D hand mesh sequence to utilize temporal information in the blurry input image, while previous works output a static single hand mesh. We demonstrate the usefulness of BlurHand for the 3D hand mesh recovery from blurry images in our experiments. The proposed BlurHandNet produces much more robust results on blurry images while generalizing well to in-the-wild images. The training codes and BlurHand dataset are available at https://github.com/JaehaKim97/BlurHand_RELEASE.