It really depends on how you define it. Here I'll refer to extrapolitical military organizations of professional soldiers who relinquished their previous lives in pursuit of a religious / philosophical agenda.

The earliest example I can think of are the Mohists in China, who were active from roughly the 5th century to 3rd century BC. Mohism is pretty hard to define, but at the time was in competition with Taoism and Confucianism as a guiding philosophy. It believed in strong form egalitarianism and utilitarianism, and sought to encourage co-existence and prevent war in order to prevent the domination of one group of humans by another. Their treatises on military defence, mathematics, and physics are sometimes held to be the birth of science in China. The Mohists formed a brotherhood of scientists and engineers, who famously offered their services to cities under attack by another. The most famous of these was the Siege of Song by Chu in c.440BC in which the Mohists simultaneously defended the city and conducted peace talks to save it.

Somewhat later, we had the Japanese sohei warrior monks. The first ones we know about came from Enryaku-ji on Mount Hiei in the 10th century. Enryaku-ji was by then one of the most powerful temples, with thousands of sub-temples, tens of thousands of monks, and a standing army numbering in the thousands. Take in mind that Enryaku-ji monks are still famous today for a hardcore form of meditation which involves walking 30km a day everyday for 1,000 days. All the largest temples soon had armies and all sorts of disputes with each other, with Mii-dera being burned down 4 times by Enryaku-ji in the 11th century alone. In the Genpei War, Mii-dera allied themselves with the Minamoto faction in one of their first military applications in the 12th century. By the 16th century, during the Sengoku Era the monks were a serious military force in their own right fighting for every side in the wars, until they were annihilated by the Oda in the massacre at Mount Hiei in 1571.

While not a professional military organisation, Shaolin Temple deserves some mention too. It's monks certainly were not often involved regularly in military disputes but trained daily to have the skills required to do so. This has been only employed officially once, in the 1550s, when the Shaolin monks were dispatched to the coast to do battle with the Japanese wokou pirates. In the famous 1553 Battle of Wenjiagang, they exterminated a force of a hundred pirates at the loss of 4 monks.