Praise be to Allah.
A rental contract is a kind of contract that is permissible in Islamic sharee’ah, according to scholarly consensus. The scholars have stated that in order for a contract to be valid, there are several conditions, such as that the usage be permissible, so it is not permissible to rent a house to one who will make it into a church or a store for selling alcohol. If it is rented for such purposes then the contract is not valid, because the usage is not permissible.
Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said: Sales of things which be used for haraam purposes are not valid, such as selling grapes to one who will use them to make wine, if that is known, as is the view of Ahmad and others, or suspected, as in one of the two views narrated from him. This is supported by the fact that our companions said: If the landlord thinks that the renter is renting the house for sinful purposes such as selling wine and the like, then it is not permissible for him to rent that house to him, and the rental contract is not valid. Sales and rentals are the same. End quote from al-Fataawa al-Kubra (5/388).
It says in Mataalib Ooli al-Nuha (3/607): It is not valid to rent out a house to be used as a church or synagogue or hermitage, or as a “fire temple” for Magian (Zoroastrian) worship, or for selling alcohol or gambling, because that is helping in sin, and Allaah says (interpretation of the meaning): “do not help one another in sin and transgression” [al-Maa’idah 5:2]; or to rent it out for music and singing, or anything that the Lawgiver has forbidden. This is the correct view. If the haraam usage is mentioned in the rental contract or is known from circumstantial evidence, the contract is invalid. So it is not permissible to rent it out to him, and the landlord of the house may prevent the dhimmi renter from selling wine in rented premises because it is a sin. End quote.
Internet cafés may be used for good or evil, but they are more often used for evil. If the person who rents the shop is keen to control it, and to forbid evil actions such as watching haraam things, visiting bad sites, smoking cigarettes and narghiles, and gambling, then it is permissible to rent the shop to him, and the income earned from that rental will be halaal.
But if the landlord knows or thinks it most likely, from what he sees of the majority of people in his city, or from the one who wants to rent the shop, that he will not control the place or prevent evil actions from taking place there, or that he will not be able to control it, or controlling it will be too difficult, because of advanced technology and different programs that enable people to go to forbidden sites, then it is not permissible for him to rent it to him, because that is helping in sin and transgression, and Allaah says (interpretation of the meaning):
“Help you one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression. And fear Allaah. Verily, Allaah is Severe in punishment”
And Allaah knows best.