The mechanism that causes the prompt-emission episode of gamma-ray bursts (GRBs) is still widely debated despite there being thousands of prompt detections. The favoured internal shock model relates this emission to synchrotron radiation. However, it does not always explain the spectral indices of the shape of the spectrum, which is often fit with empirical functions, such as the Band function. Multi-wavelength observations are therefore required to help investigate the possible underlying mechanisms that causes the prompt emission. We present GRB 121217A, for which we were able to observe its near-infrared (NIR) emission during a secondary prompt-emission episode with the Gamma-Ray burst Optical Near-infrared Detector (GROND) in combination with the Swift and Fermi satellites, which cover an energy range of 5 orders of magnitude (to). We determine a photometric redshift of with a line-of-sight with little or no extinction () utilising the optical/NIR SED. From the afterglow, we determine a bulk Lorentz factor of and an emission radius of. The prompt-emission broadband spectral energy distribution is well fit with a broken power law with and that has a break at, which can be interpreted as the maximum injection frequency. Self-absorption by the electron population below energies of suggest a magnetic field strength of. However, all the best fit models underpredict the flux observed in the NIR wavelengths, which also only rebrightens by a factor of 2 during the second prompt emission episode, in stark contrast to the X-ray emission, which rebrightens by a factor of 100. This suggests an afterglow component is dominating the emission. We present GRB 121217A, one of the few GRBs that has multi-wavelength observations of the prompt-emission period and shows that it can be understood with a synchrotron radiation model. However, due to the complexity of the GRB's emission, other mechanisms that result in Band-like spectra cannot be ruled out. © 2014 ESO.