$ sudo apt-get update
$ sudo apt-get install monodevelop-monogame 

monodevelop-monogame is installed in your system.

Make ensure the monodevelop-monogame package were installed using the commands given below,

$ sudo dpkg-query -l | grep monodevelop-monogame *

You will get with monodevelop-monogame package name, version, architecture and description in a table

monodevelop-monogame package basic information: