The results of a Fe-57 Mossbauer spectroscopy study between 2.0 and 294 K of superconducting Ba(Fe0.961Rh0.039)(2)As-2 are reported. The main component of the electric field gradient tensor at 294 K is shown to be positive and its increase with decreasing temperature is well described by a T-3/2 power-law relation. The shape of the Mossbauer spectra below the Neel temperature T-N = 55.5(1) K is shown to result from the presence of doping-induced disorder rather than of incommensurate spin-density-wave order. The measured hyperfine magnetic field reaches its maximum value at the critical temperature T-c = 14 K and then decreases by 4.2% upon further cooling to 2.0 K. This constitutes direct evidence of the coexistence of and competition between superconductivity and magnetic order. The extrapolated value of the Fe magnetic moment at 0 K is determined to be 0.35(1) mu(B). The Debye temperature of Ba(Fe0.961Rh0.039)(2)As-2 is found to be 357(3) K.