As Sandrino mentioned, startup tasks can cause this. Whenever I see that pattern, it seems that most of the time I have assemblies referenced that are on on the Azure VM that I am being deployed to.
There is a tool out there: http://gacviewer.cloudapp.net/ that will compare assemblies in your csproj file with the current Azure OS version to locate any assemblies that will need to be marked as CopyLocal=true. Note that this tool is looking at osfamily=2. VS defaults to creating osfamily=1 in your cscfg file.
This seems highly likely to me since you are deploying an MVC 4 project probably with a version of EntityFramework that is not on the Azure VM.