We prove that for α ∈ (d − 1,d), one has the trace inequality∫ℝd|IαF|dν≤C|F|(ℝd)∥ν∥Md−α(ℝd) for all solenoidal vector measures F, i.e., F∈ M _b(ℝ ^d; ℝ ^d) and divF = 0. Here I _α denotes the Riesz potential of order α and ℳ ^{d − α}(ℝ ^d) the Morrey space of (d − α)-dimensional measures on ℝ ^d.