Ensembles of micrometre-sized water droplets in a laminar oil flow are ideal systems for studying non-equilibrium dynamics. In the case of two-dimensional confinement, the interactions between the droplets’ flow-induced dipole moments lead to long-range velocity correlations and four-fold angular symmetry—behaviour that can be understood from first-principle hydrodynamics calculations. Dynamic restructuring and ordering are prevalent in driven many-body systems with long-range interactions, such as sedimenting particles1,2,3, dusty plasmas4, flocking animals5,6,7 and microfluidic droplets8. Yet, understanding such collective dynamics from basic principles is challenging because these systems are not governed by global minimization principles, and because every constituent interacts with many others. Here, we report long-range orientational order of droplet velocities in disordered two-dimensional microfluidic droplet ensembles. Droplet velocities exhibit strong long-range correlation as 1/r2, with a four-fold angular symmetry. The two-droplet correlation can be explained by representing the entire ensemble as a third droplet. The correlation amplitude is non-monotonous with density owing to excluded-volume effects. Our study puts forth a many-body problem with long-range interactions that is solvable from first principles owing to the reduced dimensionality, and introduces new experimental tools to address open problems in many-body non-equilibrium systems9,10.