Two-dimensional periodic arrays of metal dipole nanoparticles support excitation of narrow collective resonances, which can be used for enhanced light reflection or transmission and for sensing applications. With growing particle sizes, the width of collective dipole resonances is increased, approaching the width of localized surface plasmon resonance of a single particle. However, in systems with broad collective dipole resonances, much narrower resonances can be obtained due to higher multipole radiation coupling between particles. Here we developed a theoretical (semianalytical) approach for investigations of the collective (diffractive) coupling between dipole and quadrupole modes of isolated metal particles arranged in infinite or finite-size arrays. This approach is based on a solution of coupled dipole-quadrupole equations, where the dipole and quadrupole polarizabilities of individual particles are determined by Mie theory. The radiative quadrupole coupling between the particles is introduced by the full-wave quadrupole propagator. Extinction and scattering cross sections of nanoparticle arrays with dipole-quadrupole interactions are presented and discussed. The developed approach is applied for investigations of light transmission through two-dimensional hexagonal arrays of gold nanoparticles. It is shown that the quadrupole coupling can produce narrow collective resonances on the dipole background in the transmission spectra. Sensing properties of the quadrupole resonances are discussed.