We report experimental measurements of critical disorder in weakly disordered, one-dimensional photonic crystals. We measure the configurationally averaged transmission at various degrees of weak disorder. We extract the density of states (DoS) after fitting the transmission with theoretical profiles, and identify the Lifshitz tail realized by weak disorder. We observe the vanishing of Van Hove singularities and the flattening of the DoS with increasing disorder in our system. Systematic variation of disorder strength allows us to study the behavior of Lifshitz exponent with the degree of disorder. This provides a direct handle to the critical disorder in the one-dimensional crystal, at which the transport behavior of the system is known to change. The contradictory behavior at very weak disorder in the DoS variation at the band edge and the midgap are seen to resolve into synchronous behavior beyond the critical disorder. The experimentally measured transmission is shown to carry a clear signature of the critical disorder, which is in very good agreement with the theoretically expected disorder.