We report the magnetoelastic properties of a Ba2CuGe2O7 single crystal at low temperatures under a magnetic field applied along the crystallographic [001] axis. Our results extend to low temperatures, the H-T phase diagram determined for this compound by neutron scattering. Furthermore, we observe that specific elastic modes are more sensitive to the various magnetic transitions. In particular, we observe an unusual coupling between the transverse acoustic mode in the (001) plane and the cycloidal order at low field, which suggests a spin-strain mechanism originating from Dzyaloshinskii-Moriya interaction in this compound.