Official C++ language subsets
Not long ago I listened to this SE-Radio podcast - Episode 152: MISRA with Johan Bezem, which introduces MISRA, standard guidelines for C and C++ to ensure better quality, try looking at it.
Google publishes its internal C++ style guide, which is often referred to as such a subset: https://google.github.io/styleguide/cppguide.html . Ben Maurer, whose company reCAPTCHA was acquired by Google, describes it as follows in this post on Quora:
You can basically think of Google's C++ subset as C plus a bit of sugar:
The ability to add methods to structs
Basic single inheritance.
Collection and string classes
Scope based resource management.
They also publish a lint tool, cpplint.py.
There is Embedded C++. It sounds mostly similar to what you're looking for.
The GCC developers are about to allow some C++ features. I'm not aware of any official guidelines, yet, but I am pretty sure that they will define some. Have a look at initial report on the mailing list.