This paper proposes a discrete-time flux observer for the induction machine. The observer is based on a discretization of the continuous-time space-phasor flux description facilitated by a Jordan factorization of the system matrix. The proposed observer requires no assumption of stepwise constancy of the input voltage and can be modified to be especially well suited for the case of sinusoidal inputs. This makes the observer an effective tool in, for example, monitoring applications where the proposed observer is shown to yield accurate flux estimates at considerably lower sampling rates than has been possible with conventional methods. Numerical examples, as well as experimental runs, show comparisons of the proposed observer and a well-known discrete-time observer