Uncovering causal mediation effects is of significant value to practitioners who aim to isolate treatment effects from potential mediator effects. We propose a double machine learning (DML) algorithm for mediation analysis that supports continuous treatments. To estimate the target mediated response curve, our method employs a kernel-based doubly robust moment function for which we prove asymptotic Neyman orthogonality. This allows us to obtain an asymptotic normality with nonparametric convergence rate while allowing for nonparametric or parametric estimation of the nuisance parameters. Subsequently, we derive an optimal bandwidth strategy along with a procedure to estimate asymptotic confidence intervals. Finally, to illustrate the benefits of our method, we provide a numerical evaluation of our approach on a simulation along with an application on medical real-world data to analyze the effect of glycemic control on cognitive functions.