Due to a major shortage of nurses in the U.S., future healthcare service robots are expected to be used in tasks involving direct interaction with patients. Consequently, there is a need to design nursing robots with the capability to detect and respond to patient emotional states and to facilitate positive experiences in healthcare. The objective of this study was to develop a new computational algorithm for accurate patient emotional state classification in interaction with nursing robots during medical service. A simulated medicine delivery experiment was conducted at two nursing homes using a robot with different human-like features. Physiological signals, including heart rate (HR) and galvanic skin response (GSR), as well as subjective ratings of valence (happy-unhappy) and arousal (excited-bored) were collected on elderly residents. A three-stage emotional state classification algorithm was applied to these data, including: (1) physiological feature extraction; (2) statistical-based feature selection; and (3) a machine-learning model of emotional states. A pre-processed HR signal was used. GSR signals were nonstationary and noisy and were further processed using wavelet analysis. A set of wavelet coefficients, representing GSR features, was used as a basis for current emotional state classification. Arousal and valence were significantly explained by statistical features of the HR signal and GSR wavelet features. Wavelet-based de-noising of GSR signals led to an increase in the percentage of correct classifications of emotional states and clearer relationships among the physiological response and arousal and valence. The new algorithm may serve as an effective method for future service robot real-time detection of patient emotional states and behavior adaptation to promote positive healthcare experiences.