Yes this is possible. Please have a look at Mendix for Private Cloud and the various On Premise options in the Deployment category of the documentation.
There are several managed and unmanaged options available to you. I would highly recommend the managed options to ensure that you keep the value of the managed platform features such as analytics.
There is also the option to go with Private Mendix Platform, which basically means running the Mendix platform (incluyding one-click deployment, private marketplace, etc.) on an air-gapped (on prem) environment. It does come with some significant costs, though...
Hello!
As mentioned by Sebastiaan and Bart, it is possible.
However, the question to be asked is: is it really mandatory to have Mendix On-prem?
Maybe you need to comply with stricted requirements (compliance, additional security, or others) and that's the way to go, but you need to consider additional costs such as infrastructure costs, maintenance, or expert services.
If not, opting by the Mendix Private Cloud could prove to be more cost-efficient for the use case you are trying to solve.
Hope this helps!