Background: Neck self-awareness, related to sensorimotor dysfunction, can be monitored with the Fremantle Neck Awareness Questionnaire (FreNAQ). The cross-cultural adaptation of the FreNAQ in Greek (FreNAQ-GR) and an assessment of its psychometric properties were conducted. Methods: This study included 104 participants (65 female) with non-specific chronic neck pain (NSCNP). Once the cross-cultural adaptation process of the FreNAQ-GR was complete, the testing of its construct validity was conducted via an exploratory factor analysis (EFA). The construct validity examination also included a correlational analysis with a Pain Intensity Visual Analogue Scale (PI-VAS), the Neck Disability Index (NDI), the Tampa Scale of Kinesiophobia (TSK), the Pain Catastrophizing Scale (PCS), and demographics. The internal consistency of the FreNAQ-GR was also examined. A sub-sample of participants (n = 30) completed the FreNAQ-GR again after 5–7 days. Results: The dataset was appropriate for EFA (measure of sampling adequacy KMO = 0.763 and Bartlett’s test of sphericity p < 0.001). The FreNAQ-GR demonstrated a single-factor 6-item structure (items 7–9 removed), explaining 53.69% of the common variance. Statistically significant correlations (Spearman’s) were registered between the FreNAQ-GR (both versions) and the NDI (r = 0.33/0.29, p < 0.001), the TSK (r = 0.46/0.41, p < 0.001), and the PCS (r = 0.37/0.33, p < 0.001). For the 9-item and the 6-item FreNAQ-GR, the internal consistency (Chronbach’s a/McDonald’s ω) was 0.80/0.79 and 0.826/0.816, respectively. The test–retest reliability was excellent for both versions ICC2,1 (95% CI) = 0.98/0.98 (0.97–0.99/0.95–0.99), with low error values SEM = 0.90/0.74 and MDC95% = 2.49/2.05 points. Conclusions: The FreNAQ-GR is suitable for assessing neck self-awareness in Greek-speaking patients with NSCNP.