Yes, this is possible. It is called Asymmetric Accessor Accessibility, and you can read the MSDN documentation for it on this page. The code would look something like this:
public int Age
_age = value;
However, there are a couple of important caveats to keep in mind:
Only one accessor can be modified.
Any restrictions placed on an individual accessor must be more restrictive than the accessibility level of the property itself, not less.
You cannot use accessor modifiers on an interface or an explicit implementation of an interface member.