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The Hubble constant estimated from the CMB measurements shows large disagreement with the locally measured value. This inconsistency is called the Hubble tension and is vastly studied in recent years. Early Dark Energy (EDE) gives a few percent contribution to the total energy density of the universe only at an epoch before the recombination, and it is considered as a promising solution to the tension. A simple realization of EDE is given by dynamics of a scalar field, called the EDE scalar, and models including the EDE scalar are extensively studied in the literature. In this paper, we present a novel EDE scenario based on higher-dimensional gauge theories. An extra component of gauge fields associated with a compact extra dimension behaves as the EDE scalar at low-energy and has a periodic potential, which has a similar form as potentials for pseudo Nambu-Goldstone bosons (PNGB). In a five-dimensional U(1) gauge theory, we show that a scalar field that originates from the gauge field can give EDE through its dynamics in a PNGB type potential with a suitable choice of parameters in the theory. We focus on the scenario where EDE is explained by the scalar field and clarify constraints on the fundamental parameters of the gauge theory, such as the gauge coupling, the compactification scale, and the mass parameters for matter fields. We also find that a sufficient dilution of EDE requires non-trivial relations among U(1) charges of matter fields. With specific matter contents, we numerically solve the time evolution of the scalar field and confirm that its energy density behaves as an EDE. In our scenario, the parameters of the gauge theory and predicted properties of EDE are related to each other. Thus, the cosmological restrictions on the EDE properties provide insights into higher-dimensional gauge theories.