You have to update your Google Play Services and Google Repository from the Standalone SDK Manager.
Edit: As of the latest version of Android Studio the Standalone SDK Manager is removed. You must go to the SDK Tools tab.
First off, open Android Studio and click this icon at the top toolbar:
Then, when the dialog launches, click "Launch Standalone SDK Manager" at the bottom left of the dialog:
To make sure nothing other than what we want gets updated/installed, click "Deselect All":
When the Standalone SDK Manager window opens, look for "Extras" and collapse it. You should see "Google Play Services" and "Google Repository" and on the right you should see "Update Available: {something}". Select these to items and click "Install".
When they're done installing, the error will go away.
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