The quasi-two-dimensional square-lattice antiferromagnet ${\mathrm{Ba}}_{2}$ Cu${\mathrm{Ge}}_{2}$ ${\mathrm{O}}_{7}$ was studied by neutron scattering and bulk magnetic techniques. An incommensurate magnetic spiral structure with the propagation vector ($1+\ensuremath{\zeta}, 1+\ensuremath{\zeta}, 0$) ($\ensuremath{\zeta}=0.027$) was observed below ${T}_{N}=3.26$ K. Magnetic ordering occurs with a two-dimensional-like critical exponent $\ensuremath{\beta}\ensuremath{\approx}0.15$. The spin dynamics can be adequately described by conventional spin-wave theory with two exchange constants: nearest-neighbor in-plane antiferromagnetic coupling ${J}_{1}\ensuremath{\approx}0.48$ meV and interplane ferromagnetic interaction ${J}_{\ensuremath{\perp}}\ensuremath{\approx}0.013$ meV. This set of exchange parameters apparently fails to explain the spiral order. The noncentrosymmetric crystal structure suggests that the incom-mensurate phase may be the result of a Dzyaloshinskii-Moriya instability of the N\'eel ground state.