The starburst plus radio hypernovae scenario presented for high-luminosity (HLIRGs) and ultraluminous IRAS galaxies (ULIRGs) in Colina & Perez-Olea (1992) is used to predict the [Fe II] 1.64 mum luminosity in these galaxies, as well as the [Fe II] 1.64 mum, radio, and Brgamma luminosity rates. These are good indicators to characterize starbursts in heavily obscured environments, i.e., buried starbursts, such as those believed to exist in HLIRGs and ULIRGs. The predicted [Fe II] 1.64 mum luminosity for HLIRGs and ULIRGs is in the range 10(40)-10(42) ergs s-1 while the rate of [Fe II] 1.64 mum to radio luminosity, with a mean value of 17, is almost independent of the initial mass function parameters. On the contrary, the [Fe II] 1.64 mum-Brgamma luminosity rate changes from 0.05 to 1.42 as a function of the slope and upper mass limit of the initial mass function. The starburst plus radio hypernovae hypothesis is consistent with the observations if a low upper mass limit of 25-30 M., is considered. However, starbursts have difficulties in explaining observed [Fe II] 1.64 mum/Brgamma ratios well above 1.4, as in NGC 7469.