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The iron-based superconductors are characterized by sizable thermal fluctuations due to high transition temperatures and small coherence lengths. We report calorimetric and transport observations for the vortex-lattice melting in the magnetic iron-pnictide superconductor RbEuFe₄As₄ with T_c ≈ 37K and dH_c2/dT ≈ 4T/K. The melting transition is seen as a sharp drop of the resistivity and a step of the specific heat at the magnetic-field-dependent temperature. The typical step height is ∼ 4-5% of the zero-field jump, similar to YBa₂Cu₃O₇ and in agreement with theoretical estimates. The specific-heat peak due to the latent heat expected for very clean materials, however, was not observed. The melting line lies in the temperature/magnetic-field plane noticeably below the upper-critical-field line, and the vortex-liquid state occupies a significant portion of the phase diagram. The location of the melting transition is in quantitative agreement with theoretical predictions without fitting parameters.