What you need to do is go ahead and edit this file:
/Applications/IntelliJ IDEA 13.app/Contents/Info.plist
Replacing this:
<key>JVMVersion</key>
<string>1.6*</string>
with this:
<key>JVMVersion</key>
<string>1.7*</string>
Edit: As said by intellij member @crazycoder, the recomended way to total fix this is to install the latest jdk 1.6