Can a Muslim set up a shop on land that is part of the mosque property?
If this land on which he wants to build a private shop is land that was given as a waqf (endowment) for the mosque – meaning that it is part of the mosque that was built for prayer, or it is part of its environs – then it is not permissible to use it for private enterprises and personal matters under any circumstances. Rather that comes under the heading of offence and transgressing against the rights of Allah and against the rights of the Muslims.
But if it is land that was given as a waqf to be used to generate funds for the mosque, then there is nothing wrong with setting up a shop on it, but it cannot be owned by anyone; rather it remains as a waqf for the mosque, and any income generated from it should be spent on the mosque or on other good causes, according to the conditions stipulated by the one who set up the waqf.
Shaykh Ibn Baz (may Allah have mercy on him) was asked:
What is the ruling on building a home in the land surrounding the mosque [that is part of the mosque property] to live in it, noting that this land is a part of the mosque hall in which prayers in congregation are offered. If this building is completed, then what must those in charge of the mosque do?
He (may Allah have mercy on him) replied:
Nothing should be built on the mosque land. If the land belongs to the mosque, nothing should be built on it; rather it should be left as overflow space for the mosque where people can pray if there are large numbers of people, and nothing should be taken from it. Rather it should be left as extra space for the mosque. If something is needed for the imam or the mu’adhdhin, or for a library or any other purpose that is connected to the mosque, then it should be outside the mosque. It should be built outside the mosque, if there is space, or some land should be purchased to build it there, with the help of some charitable people. The point is that the extra space connected to the mosque should be left as overflow space for it."(Majmu‘ Fatawa Ibn Baz 30/83-84).
And Allah knows best.