Quantum field theory conserves mass-energy, so the new mass is coming from the energy in the Higgs field itself. It settles to a lower energy state and basically transfers that energy as mass to all of the particles that couple with it. Since it's mass-energy and not just mass that generates gravitational distortions, the large-scale gravitational evolution of the universe probably won't change, as this just moves things around a bit. It's not creating energy out of nothing.