There is no such instruction in CIL (http://www.ecma-international.org/publications/standards/Ecma-335.htm).
Assuming we can add one, an another implementation of this could be that in the Type's VTable we make the default constructor be indexed at index 0, and then the JIT can assume this information and emit code that does a VTable lookup, pick index 0 and call the function located at address pointed by this entry 0 in the VTable.
As you can see this requires a change in CLR data structures, possibly each object's layout, and likely a different solution for value types (I'm ignoring that case, because you specifically say class and new().