Enzyme-catalyzed reactions are fundamental to almost all biochemical processes occuring inside living cells. The traditional description of enzyme kinetics is a macroscopic one, in terms of a set of coupled ordinary differential equations with the implicit assumptions of the homogeneity of the medium in which the reactions occur and of large molecular concentrations. However inside cells both of these assumptions do not generally hold. In particular reactions occur in sub-cellular compartments and frequently involve small concentrations of molecules. We develop an alternative stochastic and mesoscopic description of enzyme kinetics forsuch cases and show that at typical intracellular spatial scales, the traditional description breaks down and new rate laws are valid. This has implications for both modelling of in vivo biochemical networks and for analysis of kinetics data.