Realms error: "Your client is outdated..."

I am using Minecraft 1.7.9. I am not using any "mods" or "resource packs." The only thing I am using, different from Mojang defaults, is a skin for my avatar.

For the last few days, every time I try to access "Minecraft Realms" now, I get an error: "Your client is outdated, please consider updating it to use realms."

Steps to Reproduce:
1. Open Minecraft
2. Click Minecraft Realms