Summary: The matching energy of a graph is defined as the sum of the absolute values of the zeros of its matching polynomial. A \(k\)-tree is either a complete graph on \(k\) vertices or a graph obtained from a smaller \(k\)-tree by adjoining a new vertex together with \(k\) edges connecting the new vertex to a \(k\)-clique. Let \(\mathcal{T}^k_n\) be the set of the \(k\)-trees of order \(n\), where \(n\geq k\). In \(\mathcal{T}^k_n\) with \(n\geq k+5\), the graphs with the first, the second, and the third smallest matching energies are obtained.