The following Wikipedia text shows the important contribution of Arab specialists in the booze distillery art :

The first evidence of distillation comes from Babylonia and dates from the 2nd millennium B.C. Specially shaped clay pots were used to extract small amounts of distilled alcohol through natural cooling for use in perfumes. By the 3rd century A.D., alchemists in Alexandria, Egypt, may have used an early form of distillation to produce alcohol for sublimation or for colouring metal.[citation needed]
Alcohol was distilled for the first time by Arab and Persian chemists in the 8th and 9th centuries.[3] The development of the still with cooled collector—necessary for the efficient distillation of spirits without freezing—was an invention of alchemists during this time. In particular, Geber (Jabir Ibn Hayyan, 721–815) invented the alembic still; he observed that heated wine from this still released a flammable vapor, which he described as "of little use, but of great importance to science". Not much later Al-Razi (864–930) described the distillation of alcohol and its use in medicine. By that time, distilled spirits had become fairly popular beverages: the poet Abu Nuwas (d. 813) describes a wine that "has the colour of rain-water but is as hot inside the ribs as a burning firebrand". The terms "alembic" and "alcohol", and possibly the metaphors "spirit" and aqua vitae (“water of life”) for the distilled product, can be traced to Arabic alchemy.[3]

But in spite of those specialists mostly to have been Muslims, it has nothing to do with Islam but with Arab science. And at the beginning also with Persian science.