Recent gravitational wave observations from the merging black holes (BHs) and neutron stars have provided a unique opportunity to study the behavior of gravity in the highly nonlinear and dynamical regime. We propose a novel method to test the consistency of the multipole moments of compact binary systems with the predictions of General Relativity (GR) within the Post-Newtonian (PN) formalism. For nonspinning compact binaries, we derive the gravitational wave phasing formula, in the frequency domain, parametrizing each PN order term by scaling the multipole moments with free parameters. Using GW observations, this parametrized multipolar phasing would allow us to derive the bounds on possible departures from the multipole structure of GR and hence constrain the parameter space of alternative theories of gravity. We compute the projected constraints on the multipole parameters for the second generation ground-based detectors, such as Advanced Laser Interferometer Gravitational-wave Observatory (LIGO), the third generation detectors such as Einstein Telescope and Cosmic Explorer, as well as space-based detector Laser Interferometer Space Antenna (LISA). We find that while Advanced LIGO can measure the first two or three multipole coefficients with good accuracy, Cosmic Explorer and Einstein Telescope may be able to measure the first four multipole coefficients which enter the phasing formula. Intermediate mass ratio inspirals, with mass ratio of several tens, in the frequency band of planned space-based LISA mission should be able to measure all the seven multipole coefficients which appear in the 3.5PN phasing formula. The proposed test will facilitate the first probe of the multipolar structure of Einstein's general relativity.