I had this problem earlier. In my case, the kernel I elected to use when booting my droplet was an *older* kernel. Then I performed various updates which included installing a *newer* kernel. When you do that, all the libraries are setup for the new kernel, but digital ocean doesn't use the new kernel, it uses the one you specify in your droplet configuration.
When I bumped the droplet configuration kernel up to the same one I had just updated to in my instance, iptables began to work again.
Now here's the key. When you get this working again, setup your kernel package to be "fixed" and not auto-upgradable. If you decide to upgrade, in the future, you have to do *both*, pick the droplet configuration kernel version you like, and then in your package manager, remove the old and pick the "fixed" package that exactly corresponds.