In-service monitoring and adaptive digital compensation of analog imperfections in optical transponders are vital in the next-generation optical coherent transmission systems employing extremely high-order, high-speed modulation formats. A notable example of such analog impairments is the imbalance of amplitude, phase, and/or timing between the in-phase (I) and quadrature (Q) tributaries in an optical IQ modulator, namely the IQ imbalance. Recently, an IQ-imbalance estimation technique based on phase retrieval without using a coherent receiver, the so-called single-pixel optical modulation analyzer (SP-OMA), has been proposed as an affordable in-service monitoring solution for the frequency-dependent IQ imbalance in a (single-polarization) IQ modulator. In this work, we extend the concept of the SP-OMA to dual-polarization IQ modulators. A novel phase retrieval algorithm with an alternating minimization procedure is proposed for identifying the frequency-dependent IQ imbalances on both polarization channels simultaneously from a single photodetector output. The validity and feasibility of the proposed SP-OMA for a dual-polarization IQ modulator are demonstrated numerically and experimentally with a 63.25-Gbaud DP-16QAM signal.