A network-based data store maintaining storage volumes for file systems at storage clients may implement dynamic storage volume scaling. A scaling event may be detected according to a specified scaling policy for a storage volume maintained at a network-based data store that is mounted at a storage client and configured for a file system. In a least some embodiments, the scaling policy for the storage volume may be received from the storage client. In response to detecting the storage event, storage maintaining the storage volume may be modified according to the scaling policy to scale the storage volume. An indication of the scaling event may be sent to the storage client in order to update the file system at the storage client so that the file system may utilize the scaled storage volume.