This paper is concerned with finite horizon risk-sensitive filtering, prediction and smoothing problem for discrete-time singular systems. The problem is first converted to a minimax optimization of certain indefinite quadratic form. It is shown that a risk-sensitive estimator can be obtained by ensuring the minimum of the indefinite quadratic form to be maximum (minimum) when the risk-sensitivity parameter Θ is negative (positive). An auxiliary state-space signal model and innovation sequences in Krein space are introduced to simplify our derivation. The finite horizon estimator is given based on a recursive Riccati equation by constructing a appropriate state space model.