Presence of malicious injection originating from cyber attacks in PMU measurements can potentially affect the operation and stability of power system. This paper presents a method for detecting malicious data injections in PMU measurements. The problem of detection of malicious injections is formulated as a compressed sensing problem and the corrupted signals are recovered using a robust PCA-based algorithm. Different patterns of malicious injection attacks on PMU data are considered and the effect of corruption and reconstruction using the algorithm is analyzed on a wide-area oscillation monitoring application. Data from a 16-machine, 5-area New England-New York system is used along with a recursive oscillation monitoring algorithm to test and validate the effectiveness of the proposed approach on correct detection and reconstruction of the PMU signals under both ambient and transient conditions.