Resonant electric dipole-dipole interactions between cold Rydberg atoms were observed using microwave spectroscopy. Laser-cooled Rb atoms in a magneto-optical trap were optically excited to 45d Rydberg states using a pulsed laser. A microwave pulse transferred a fraction of these Rydberg atoms to the 46p state. A second microwave pulse then drove atoms in the 45d state to the 46d state, and was used as a probe of interatomic interactions. The spectral width of this two-photon probe transition was found to depend on the presence of the 46p atoms, and is due to the resonant electric dipole-dipole interaction between 45d and 46p Rydberg atoms.