Turbulent mixing at centimetre scales is an essential component of the ocean’s meridional overturning circulation and its associated global redistribution of heat, carbon, nutrients, pollutants and other tracers. Whereas direct turbulence observations in the ocean interior are limited to a modest collection of field programs, basic information such as temperature, salinity and depth ($T,S,Z$) is available globally. Here, we show that supervised (deep) machine learning algorithms, informed by physical understanding, can be trained on the existing turbulence data to develop skillful predictions of the key properties of turbulence from $T,S,Z$ and topographic data. This constitutes a promising first step toward a hybrid physics - artificial intelligence approach to parameterize turbulent mixing in climate-scale ocean models.