We have studied the solvation of model peptides at low hydration levels by terahertz absorption spectroscopy. We have recorded the concentration-dependent terahertz absorption coefficients of N-acetyl-glycine-amide (NAGA), N-acetyl-glycine-methylamide (NAGMA), N-acetyl-leucine-amide (NALA), N-acetyl-leucine-methylamide (NALMA), and N-acetyl-tryptophan-amide (NATA) in aqueous solution. We find a dramatic decrease in the THz absorption, if the number of water molecules per solute is less than 18-20. This change is taken as a signature for the breakdown of peptide-water network motions, which supports the hypothesis that a minimum number of hydration waters is required to activate these motions. This is well below a monolayer coverage of the model peptides. It is interesting to note that the required hydration level corresponds to the number of water molecules which are required for biological functionality.