On December 27th 2004, a giant γ-flare from the Soft Gamma-ray Repeater 1806-20 saturated many satellite gamma-ray detectors. This event was by more than two orders of magnitude the brightest cosmic transient ever observed. If the gamma emission extends up to TeV energies with a hard power law energy spectrum, photo-produced muons could be observed in surface and underground arrays. Moreover, high-energy neutrinos could have been produced during the SGR giant flare if there were substantial baryonic outflow from the magnetar. These high-energy neutrinos would have also produced muons in an underground array. AMANDA-II was used to search for downgoing muons indicative of high-energy gammas and/or neutrinos. The data revealed no significant signal. Upper limits on the normalization constant of the gamma flux were determined for different spectral indices γ. For γ = −1.47 (−2), the limit is 0.05 (0.5) TeV m s at 90% CL. Similarly, we set limits on the normalization constant of the high-energy neutrino emission of 0.4 (6.0) TeV m s for γ = −1.47 (−2).