We predict, using a free-energy calculation, that the quantum phase transition between the U(1) quantum spin liquid (QSL) and antiferromagnet (AFM) phases in certain pyrochlore quantum spin ice is first order rather than second order. This change in order from second to first order is induced by gauge fluctuations, which are explicitly taken into account at gauge theory level in our effective low-energy theory. We therefore have identified a fluctuation-induced first-order quantum phase transition in pyrochlore quantum spin ice. We explicitly derive the quantum free-energy description of this QSL-to-AFM phase transition and predict that it is a weakly first-order phase transition. We also briefly discuss the experimental relevance of this result.