An EXE setup file can be anything, including an MSI in a setup.exe launcher. However, in your case I don't believe that is the case. You probably have a legacy non-MSI installer.
Most big companies actually take older, legacy-style setups and repackage them as MSI themselves - whole teams exist to do this job (as mentioned by Linda). This is to benefit from a substantial number of MSI benefits for corporate use that are crucial for large scale deployment (the administration of software for many computers). See the same link for common problems with MSI files - it is definitely not an easy technology to deal with.
Wrapping your existing EXE in an MSI is not an option. This adds nothing but risk and complexity for no gain at all. In fact you will irritate application packagers in large companies by making it harder to repackage the right way.
Remaking your setup to be an MSI file is a good investment if you use good consultants to do it, or take the time to train your developers to do it right. MSI is an unusual technology, and distinctively unorthodox to deal with. Many developers feel it is impossible to understand, and for good reason. It is an entirely different installation paradigm than what used to be.
The latest and greatest for MSI is the Wix toolkit. A free open-source toolkit allowing you to create full-fledged MSI files without any expensive third-party tools. This short summary of its history and creation might be helpful to understand what MSI is about as well.
I guess the overall summary is that wrapping your software in an MSI file is no small investement with regards to the work involved, but it has major benefits when done right.
Wrapping your existing EXE inside an MSI has no value at all - it just causes new problems.