Background: The COVID-19 pandemic has accelerated the demand for utilising telehealth as a major mode of healthcare delivery, with increasing interest in the use of tele-platforms for remote patient assessment. In this context, the use of smartphone technology to measure squat performance in people with and without femoroacetabular impingement (FAI) syndrome has not been reported yet. We developed a novel smartphone application, the TelePhysio app, which allows the clinician to remotely connect to the patient’s device and measure their squat performance in real time using the smartphone inertial sensors. The aim of this study was to investigate the association and test–retest reliability of the TelePhysio app in measuring postural sway performance during a double-leg (DLS) and single-leg (SLS) squat task. In addition, the study investigated the ability of TelePhysio to detect differences in DLS and SLS performance between people with FAI and without hip pain. Methods: A total of 30 healthy (nfemales = 12) young adults and 10 adults (nfemales = 2) with diagnosed FAI syndrome participated in the study. Healthy participants performed DLS and SLS on force plates in our laboratory, and remotely in their homes using the TelePhysio smartphone application. Sway measurements were compared using the centre of pressure (CoP) and smartphone inertial sensor data. A total of 10 participants with FAI (nfemales = 2) performed the squat assessments remotely. Four sway measurements in each axis (x, y, and z) were computed from the TelePhysio inertial sensors: (1) average acceleration magnitude from the mean (aam), (2) root-mean-square acceleration (rms), (3) range acceleration (r), and (4) approximate entropy (apen), with lower values indicating that the movement is more regular, repetitive, and predictable. Differences in TelePhysio squat sway data were compared between DLS and SLS, and between healthy and FAI adults, using analysis of variance with significance set at 0.05. Results: The TelePhysio aam measurements on the x- and y-axes had significant large correlations with the CoP measurements (r = 0.56 and r = 0.71, respectively). The TelePhysio aam measurements demonstrated moderate to substantial between-session reliability values of 0.73 (95% CI 0.62–0.81), 0.85 (95% CI 0.79–0.91), and 0.73 (95% CI 0.62–0.82) for aamx, aamy, and aamz, respectively. The DLS of the FAI participants showed significantly lower aam and apen values in the medio-lateral direction compared to the healthy DLS, healthy SLS, and FAI SLS groups (aam = 0.13, 0.19, 0.29, and 0.29, respectively; and apen = 0.33, 0.45, 0.52, and 0.48, respectively). In the anterior–posterior direction, healthy DLS showed significantly greater aam values compared to the healthy SLS, FAI DLS, and FAI SLS groups (1.26, 0.61, 0.68, and 0.35, respectively). Conclusions: The TelePhysio app is a valid and reliable method of measuring postural control during DLS and SLS tasks. The application is capable of distinguishing performance levels between DLS and SLS tasks, and between healthy and FAI young adults. The DLS task is sufficient to distinguish the level of performance between healthy and FAI adults. This study validates the use of smartphone technology as a tele-assessment clinical tool for remote squat assessment.