The ultrafast vibrational dynamics of HDO:D2O ice at 180 K in anionic reverse micelles is studied by midinfrared femtosecond pump-probe spectroscopy. Solutions containing reverse micelles are cooled to low temperatures by a fast-freezing procedure. The heating dynamics of the micellar solutions is studied to characterize the micellar structure. Small reverse micelles with a water content up to approximately 150 water molecules contain an amorphous form of ice that shows remarkably different vibrational dynamics compared to bulk hexagonal ice. The micellar amorphous ice has a much longer vibrational lifetime than bulk hexagonal ice and micellar liquid water. The vibrational lifetime is observed to increase linearly from 0.7 to 4 ps with the resonance frequency ranging from 3100 to 3500 cm-1. From the pump dependence of the vibrational relaxation the homogeneous linewidth of the amorphous ice is determined (55±5 cm-1).