Luckily, I came across a great little post from webupd8.org that I've summarized below (should the post ever be removed). In either case, this post is for anyone wishing to disable IPv6 on their Ubuntu server.
1. Check if the IPv6 stack is enabled. The stack is enabled if the return is 0.
$ cat /proc/sys/net/ipv6/conf/all/disable_ipv6
2. Elevate to root and open your /etc/sysctl.conf file in nano.
$ sudo nano /etc/sysctl.conf
3. Paste the following at the end of the sysctl.conf:
#disable ipv6
net.ipv6.conf.all.disable_ipv6 = 1
net.ipv6.conf.default.disable_ipv6 = 1
net.ipv6.conf.lo.disable_ipv6 = 1
4. Reboot and perform step 1. If you find the return to still be 0, head over to the webupd8 link above to see the other methods they have listed.