This study aimed to assess the impact of the COVID-19 pandemic on general practitioner (GP), specialist, and dentist visits among 40 million Iranians covered by the Social Security Organization (SSO). A monthly interrupted time series analysis was conducted over a period of 72 months, including—47 months before the pandemic and 25 months after its onset. The outcomes variables were monthly number of GP, specialist, and dentist visits per 1000 SSO-insured individuals. The analysis was performed by total visits, visits to the SSO direct sector, and visits to the indirect sectors. The study found that in the first month of the pandemic, the number of visits per 1000 insured individuals significantly decreased for visits to GPs (by 51.12, 95% CI −64.42 to −37.88), visits to specialists (by 39.11, 95% CI −51.61 to −26.62), and visits to dentists (by 6.67, 95% CI −8.55 to −4.78). However, during the subsequent months of the pandemic, there was a significant increase in the number of monthly visits for all three categories, with GPs experiencing the highest increase (1.78 visits per 1000 insured), followed by specialists (1.32 visits per 1000 insured), and dentists (0.05 visits per 1000 insured). Furthermore, prior to the pandemic, the number of monthly GP visits per 1000 insured individuals was statistically significantly lower in the indirect sector compared to the direct sector (45.79, 95% CI −52.69 to −38.89). Conversely, the direct sector exhibited lower rates of specialist visits (25.84 visits per 1000 insured individuals, 95% CI 22.87 to 28.82) and dentist visits (0.75 visits per 1000 insured individuals, 95% CI 0.12 to 1.36) compared to the indirect sector. Additionally, the study found that in the first month of the pandemic, the monthly number of GP visits in the indirect sector significantly increased by 34.44 times (95% CI 24.81 to 44.08) compared to the direct sector. For specialist visits and dentist visits, the increase was 3.41 (95% CI −5.87 to 12.69) and 5.01 (95% CI 3.48 to 6.53) per 1000 insured individuals, respectively. Overall, the findings of this study demonstrate statistically significant disruptions in GP, specialist, and dentist visits during the COVID-19 pandemic, although some recovery was observed. Both the direct and indirect sectors experienced decreased visits.