A key requirement of an autonomous self-replicating molecular machine, a protocell, is the ability to digest resources and turn them into building blocks. Thus a protocell needs a set of metabolic processes fueled by external free energy in the form of available chemical redox potential or light. We introduce and investigate a minimal photodriven metabolic system, which is based on photofragmentation of resource molecules catalyzed by genetic molecules. We represent and analyze the full metabolic set of reaction-kinetic equations and, through a set of approximations, simplify the reaction kinetics so that analytical expressions can be obtained for the building block production. The analytical approximations are compared with the full equation set and with corresponding experimental results to the extent they are available. It should be noted, however, that the proposed metabolic system has not been experimentally implemented, so this investigation is conducted to obtain a deeper understanding of its dynamics and perhaps to anticipate its limitations. We demonstrate that this type of minimal photodriven metabolic scheme is typically rate-limited by the front-end photoexcitation process, while its yield is determined by the genetic catalysis. We further predict that gene-catalyzed metabolic reactions can undergo evolutionary selection only for certain combinations of the involved reaction rates due to their intricate interactions. We finally discuss how the expected range of metabolic rates likely affects other key protocellular processes such as container growth and division as well as gene replication.