Plasmonic biosensors, particularly arrays of nanoholes on thin gold films, have been widely explored in recent years as possible platforms for fast medical diagnostic. In this work, we present a screening method for leukemia cancer markers that uses a plasmonic biosensor based on nanohole arrays fabricated on plastic substrates. The low-cost, scalable, and reproducible nanohole array structures were fabricated by UV nanoimprinting technique. The relative concentration of human immunoglobulin kappa and lambda light chains in blood serum was employed as a screening method. The kappa/lambda concentration ratio was used to determine an unbalance in the immunoglobulin production due to leukemia. The platform was tested using serum samples from patients with known leukemia diagnoses. The results indicated that this inexpensive and flexible plasmonic platform is a promising tool for routine screening in clinical settings.