This situation is referred to as  Pseudo-first order kinetics, and is confirmed when First order kinetics are observed for the drug disappearance.
Also applies for reactions involving  acid (H3O+ )  or  base  (OH- ) when high concentrations or buffers are used in the reaction solution thereby maintaining the reagent at constant concentration.
Sometimes, a reaction can be observed to follow ZERO order kinetics
-  d [ D ] / dt = k0 
eg,  a sparingly soluble drug undergoes degradation in solution - in the presence of solid drug, the solution concentration remains constant at the saturation solubility.