The noncontact blade tip timing (BTT) measurement has been an attractive technology for blade health monitoring (BHM). However, the severe undersampled BTT signal causes a significant challenge for blade vibration parameter identification and fault feature extraction. This study proposes a novel method based on the minimum variance distortionless response (MVDR) of the direction of arrival (DoA) estimation for blade natural frequency estimation from the non-uniformly undersampled BTT signals. First, based on the similarity between the general data acquisition model for BTT and the antenna array model in DoA estimation, the circumferentially arranged probes on the casing can be regarded as a non-uniform linear array. Thus, BTT signal reconstruction is converted into the DoA estimation problem of the non-uniform linear array signal. Second, MVDR is employed to address the severe undersampling issue and recover the BTT undersampled signal. In particular, spatial smoothing is innovatively utilized to enhance the estimation of covariance matrix of the BTT signal to avoid ill-condition or singularity, while improving efficiency and robustness. Lastly, numerical simulation and experimental testing are employed to verify the validity of the proposed method. Monte Carlo simulation results suggest that the proposed method behaves better than conventional methods, especially under a lower signal-to-noise ratio condition. Experimental results indicate that the proposed method can effectively overcome the severe undersampling problem of BTT signal induced by physical limitations, and has a strong potential in the field of BHM.