We show that a block interleaved maximum distance separable (MDS) code offers near-optimal burst erasure protection, in the sense that no other scheme of equal total transmission length and code rate could improve the guaranteed-correctible burst erasure length by more than one symbol. The optimality does not depend on the length of the code, i.e., a short MDS code block interleaved to a given length would perform as well as a longer MDS code of the same overall length. As a result, this approach offers lower decoding complexity with better burst erasure protection compared to other recent designs for the burst erasure channel (e.g., low-density parity-check codes). A limitation of the design is its lack of robustness to channels that have impairments other than burst erasures (e.g., additive white Gaussian noise), making its application best suited for correcting data erasures in layers above the physical layer.