I speak of the Middle Ages.

Islam doesn't really have monasticism. Within Sufism, Islam's mystical tradition, we can see some parallels to Christian monasticism, but fundamental differences remain--they are, at heart, different institutions with different roles to play in their respective religions and societies.

According to Christian tradition, the roots of monasticism lie in the late antique Egyptian desert, where so-called Desert Fathers (and Mothers!) were inspired to (in theory) leave "the world" behind, and move into isolated (in theory) caves or rough buildings to focus on their spiritual lives and relationships with God. Two things happened: one, they were seen as holy and people from nearby villages/cities came to them seeking advice and consolation. Two, they started to form their own communities. First, communities of hermits who sometimes came together; eventually, communities who devoted as much time to seeking God as a community (in group prayer) as on their own. And, eventually, these communities developed formal Rules to regulate their daily lives.

That is what we typically mean by "monasticism" in Christianity: a group of people, typically single-sex (although "double-houses" of women and men, isolated from each other but living side-by-side, are a western medieval thing in certain times and places), who swear permanent vows of poverty, chastity, and obedience; wear a uniform; and follow a rigid daily schedule of group prayer, individual prayer, and some amount of time for work.

As a social institution, monasteries own land, play power politics, are played with in power politics among bishops and secular lords (donating land to a monastery to keep it out of someone else's hands), offer a place for noble and royal widows to finish out their lives without needing to remarry (and thus preventing their lands from leaving the family), provide charity, and intercede between their patrons and God. In the early Middle Ages, monasteries were crucial in spreading and anchoring Christianity across pagan Europe. They were centers of learning, literacy, and libraries throughout the medieval world. As a religious institution, monasteries allow monks and nuns to nurture their inner spiritual lives--Christian mysticism largely, though not exclusively, comes out of the monastic tradition.

So in Christianity, mysticism tends to emerge from monasticism, or is just one part of it. Conversely, Sufism is the inner or mystical dimension of Islam, and in some cases, we can see some parallels to monasticism within that mysticism tradition.

The Sufi tradition generally consists of disciples or students under a leader. As you might expect, this idea of a teacher with a group of students, appointing one as their heir upon their death, does lead to the development of tariqa or orders of Sufism.

Unlike the rigid, exclusive, vowed communities of monasticism, however, Sufi orders are fluid. People can join them, leave them, adhere to multiple traditions at the same time! They are collective teachings of ways to build your individual relationship with God. The Christian monastic orders can also be seen that way, but they are exclusive, for-life, and consider the full way of life as part of building that relationship.

Adherence to Sufi orders can manifest in many different forms. In some cases, particularly in north and west Africa, where an entire people or branch of a people will follow Sufi principles. Some Sufis will live independently and come together or meet with the teacher. But in other cases, we do see Sufis living in community. I stress that this is not the formal vowed life under a Rule of Christian monasticism. Neverthless, zawiya/tekke/Sufi "lodges" of the Middle Ages resemble their Christian counterparts in some ways.

Structurally or architecturally, the zawiya complex provided lodging for their Sufis, a school (zawiya simply means madrasa/religious school in some parts of the Arab world), space for daily prayer, and sometimes institutions like lodging for visitors or hospitals for the sick and indigent. You would find equivalents for all of these in medieval Christian monasteries! Zawiyas, though, reflected Sufism's individualistic focus much more than their Christian counterparts tended to. While most Christian monastic traditions did not allow individual cells or space for private prayer until later in the Middle Ages (Christianity also has an eremetic or hermit tradition, though), Sufi zawiyas frequently offered both. And again, vows and the rigidity of monastic Rules were not part of life in a zawiya.

Sufi zawiyas did, however, mirror Christian monasteries in their missionary function. Both individual Sufis and established zawiyas played crucial roles in the expansion of both Islam and literacy in the early medieval (and also rather more modern) world.

Islam and eventually Sufism are born and cultivated partially in lands very familiar with either western or eastern forms of Christian monasticism--including, of course, the Egyptian desert itself. Were the Sufi zawiyas inspired by the Christian monastic communities their founders were well aware of? Was it simply the case that the medieval Mediterranean world shared enough circumstances that educated religious communities as beacons of charity and missionary work filled a necessary niche in both? Or was it a mix of the two? As you can imagine, influences between Christian monasticism, Sufi zawiyas, and the mystical tradition within the two religions (and Judaism as well) remains a rather hotly debated question.

Overall, it is wrong to say medieval Islam developed monasticism. But a closer look reveals that within Sufism, institutions did develop that paralleled contemporary Christian monasteries in several important respects.

My apologies for not including the Buddhist, Hindu or Jain monastic traditions in this discussion.