  Non-Markovian effects can speed up the dynamics of quantum systems while the
limits of the evolution time can be derived by quantifiers of quantum
statistical speed. We introduce a witness for characterizing the
non-Markovianity of quantum evolutions through the Hilbert-Schmidt speed (HSS),
which is a special type of quantum statistical speed. This witness has the
advantage of not requiring diagonalization of evolved density matrix. Its
sensitivity is investigated by considering several paradigmatic instances of
open quantum systems, such as one qubit subject to phase-covariant noise and
Pauli channel, two independent qubits locally interacting with leaky cavities,
V-type and $\Lambda $-type three-level atom (qutrit) in a dissipative cavity.
We show that the proposed HSS-based non-Markovianity witness detects memory
effects in agreement with the well-established trace distance-based witness,
being sensitive to system-environment information backflows.
