A new three-dimensional chemometric approach was introduced to explore the interaction of hydroxychloroquine (HCQ)-calf thymus deoxyribonucleic acid (DNA) and quantify binding constant using fluorescence excitation and emission measurements. The fluorescence excitation-emission spectra were recorded after gradual titration of HCQ with DNA. Then, the excitation and emission curves and relative concentrations of the drug and drug-DNA complex were quantitatively estimated using a three-dimensional model called Parallel Factor Analysis (PARAFAC) to a cubic fluorescence data array. The interaction of HCQ and DNA was predicted by applying newly modified Stern-Volmer equations to the relationship between the actual DNA concentration, and the HCQ concentration in the relative concentration profile of the PARAFAC model. In the PARAFAC application, the binding constants of the HCQ-DNA complex at 288, 298, and 310 K were found as 6.78 × 103, 5.07 × 103, and 3.74 × 103 L mol−1, respectively. From the temperature studies, the thermodynamic parameters (ΔS0= 3.528 J mol−1 K−1, ΔH0= −20.099 kJ mol−1 and ΔG0=-21.11, −21.12, and −21.19 kJ mol−1 at 288, 298, and 310 K, respectively) were calculated. The drug-DNA interaction is spontaneous due to negative ΔG0 values. The positive ΔS0 and negative ΔH0 values revealed the major role of the electrostatic force on the binding of HCQ to DNA. Assay results obtained from the proposed three-way modeling were compared to those provided by the traditional spectrofluorimetric method.