We study the thermodynamic notion of quantum projective measurements, using a framework for the fluctuation theorem of nonequilibrium work. The energy change induced by measurements satisfies the Jarzynski equality, leading us to the interpretation that the quantum projective measurements perform nonequilibrium work on the measured system. The work average exhibits intriguing limiting behaviors due to the heat-up effect caused by repeated measurements and the quantum Zeno effect caused by measurements of an infinite frequency. If the measured system relaxes back to its initial equilibrium state, the work is completely dissipated in the form of heat into a reservoir. The corresponding entropy increase in the reservoir is shown to be not less than the von Neumann entropy change generated during the course of the measurements, proving Landauer's principle.