Solved.
MonoMac should be compiled from sources:
- Clone https://github.com/mono/monomac (including submodules).
- Open terminal and run "make" in the root folder.
- Find MonoMac.dll in src folder and copy it to your project directory.
- Reference it directly (don't use the version bundled with Xamarin Studio).
One thing I also tried is to run NSApplication.Init() when starting the app. It seems a working solution too.