This paper addresses the problem of fault detection filter design for discrete-time Markovian jump singular systems with intermittent measurements. The measurement transmission from the plant to the fault detection filter is assumed to be imperfect and a stochastic variable is utilized to model the phenomenon of data missing. Our attention is focused on the design of a fault detection filter such that the residual system is stochastically Markovian jump admissible and satisfies some expected performances. A new necessary and sufficient condition for a class of discrete-time Markovian jump singular systems to be stochastically Markovian jump admissible is proposed in the form of strict linear matrix inequalities. Sufficient conditions are established for the existence of the fault detection filter. Finally, a numerical example is provided to demonstrate the usefulness and applicability of the developed theoretical results.