MongoDB is a relatively new technology and the most part of hosting providers tends to install well-known, largely-adopted solutions.
Probably the main cause is represented by standardized control panels such as CPanel and Plesk. Small-medium hosting providers are limited to the number of features these panels are able to provide.
For this reason, if you want to use MongoDB it's likely you need to install it on your own server or use a dedicated service.
At the time being, there are essentially 2 companies that provide a MongoDB DaaS (Database as a Service):