Background/Objectives: COVID-19 frequently causes olfactory and gustatory dysfunction, including qualitative disorders like parosmia and phantosmia. These distortions affect quality of life and may result from both peripheral and central neural damage. Despite increasing reports, their prevalence, mechanisms, and risk factors remain unclear. The purpose of this study is to evaluate the clinical characteristics and possible predictors of parosmia and phantosmia associated with COVID-19 in Saudi Arabia. Methods: This cross-sectional study utilized an online questionnaire targeting adults in Saudi Arabia with self-reported new-onset olfactory or gustatory dysfunction after COVID-19. Results: Out of 539 participants, 377 were included for analysis. Females slightly outnumbered males (195, 51.7% vs. 182, 48.3%) with a mean age of 34.5 years (SD = 12.7). Comorbidities were present in 86 (23.3%) participants, predominantly including hypertension (39.5%) and diabetes (30.2%). Sudden smell and taste loss were reported by 277 (73.5%) and 267 (70.8%) participants, respectively. Regional residence was significantly associated with both smell (p < 0.001) and taste loss (p < 0.001). Academic qualification exhibited borderline significance in relation to taste loss (p = 0.049). Logistic regression analysis indicated no significant predictors of dysfunction, with male gender exhibiting an odds ratio of 1.276 for smell (p = 0.301) and an odds ratio of 1.401 for taste (p = 0.144). Over 60% of participants experienced a negative impact on their quality of life. Conclusions: This study demonstrates the prevalence of parosmia and phantosmia in COVID-19 patients in Saudi Arabia, with a significant impact on quality of life. While regional differences and education level exhibited certain associations, no demographic or clinical factors independently predicted dysfunction, highlighting the necessity for additional research into underlying mechanisms and long-term effects.