We study the deformation of a lipid membrane in response to a local pH modification. Experimentally, a basic solution is microinjected close to a giant unilamellar vesicle. A local deformation appears in the zone of the membrane that is closest to the micropipette, and relaxes when the injection is stopped. A theoretical description of this phenomenon is provided. It takes fully into account the spatiotemporal evolution of the concentration of hydroxide ions during and after the microinjection, as well as the linear dynamics of the membrane. This description applies to a local injection of any substance that reacts reversibly with the membrane lipids. We compare experimental data obtained in the domain of small deformations to the results of our linear description, and we obtain a good agreement between theory and experiments. In addition, we present direct experimental observations of the pH profile on the membrane during and after the microinjection, using pH-sensitive fluorescent lipids.