This paper combines causal mediation analysis with double machine learning for a data-driven control of observed confounders in a high-dimensional setting. The average indirect effect of a binary treatment and the unmediated direct effect are estimated based on efficient score functions, which are robust w.r.t. misspecifications of the outcome, mediator, and treatment models. This property is key for selecting these models by double machine learning, which is combined with data splitting to prevent overfitting. We demonstrate that the effect estimators are asymptotically normal and n^−1/2-consistent under specific regularity conditions and investigate the finite sample properties of the suggested methods in a simulation study when considering lasso as machine learner. We also provide an empirical application to the U.S. National Longitudinal Survey of Youth, assessing the indirect effect of health insurance coverage on general health operating via routine checkups as mediator, as well as the direct effect.