Context. Exoplanetary research has provided us with exciting discoveries of planets around very low-mass (VLM) stars (0.08 M_⊙ ≲ M_* ≲ 0.3 M_⊙; e.g., TRAPPIST-1 and Proxima Centauri). However, current theoretical models still strive to explain planet formation in these conditions and do not predict the development of giant planets. Recent high-resolution observations from the Atacama Large Millimeter/submillimeter Array (ALMA) of the disk around CIDA 1, a VLM star in Taurus, show substructures that hint at the presence of a massive planet. Aims. We aim to reproduce the dust ring of CIDA 1, observed in the dust continuum emission in ALMA Band 7 (0.9 mm) and Band 4 (2.1 mm), along with its ¹²CO (J = 3−2) and ¹³CO (J = 3−2) channel maps, assuming the structures are shaped by the interaction of the disk with a massive planet. We seek to retrieve the mass and position of the putative planet, through a global simulation that assesses planet-disk interactions to quantitatively reproduce protoplanetary disk observations of both dust and gas emission in a self-consistent way. Methods. Using a set of hydrodynamical simulations, we model a protoplanetary disk that hosts an embedded planet with a starting mass of between 0.1 and 4.0 M_Jup and initially located at a distance of between 9 and 11 au from the central star. We compute the dust and gas emission using radiative transfer simulations, and, finally, we obtain the synthetic observations, treating the images as the actual ALMA observations. Results. Our models indicate that a planet with a minimum mass of ~1.4 M_Jup orbiting at a distance of ~9−10 au can explain the morphology and location of the observed dust ring in Band 7 and Band 4. We match the flux of the dust emission observation with a dust-to-gas mass ratio in the disk of ~10⁻². We are able to reproduce the low spectral index (~2) observed where the dust ring is detected, with a ~40−50% fraction of optically thick emission. Assuming a ¹²CO abundance of 5 × 10⁻⁵ and a ¹³CO abundance 70 times lower, our synthetic images reproduce the morphology of the ¹²CO (J = 3−2) and ¹³CO (J = 3−2) observed channel maps where the cloud absorption allowed a detection. From our simulations, we estimate that a stellar mass M_* = 0.2 M_⊙ and a systemic velocity v_sys = 6.25 km s⁻¹ are needed to reproduce the gas rotation as retrieved from molecular line observations. Applying an empirical relation between planet mass and gap width in the dust, we predict a maximum planet mass of ~4−8 M_Jup. Conclusions. Our results suggest the presence of a massive planet orbiting CIDA 1, thus challenging our understanding of planet formation around VLM stars.