(1) Background: Endometriosis is a frequent chronic pain condition in women of fertile age. Pain management with analgesics is frequently used by women with endometriosis. During the COVID-19 pandemic, access to health services was temporarily restricted in various countries for persons without serious conditions, resulting in increased physical and mental health issues. The present study was conducted in order to assess the risk factors predicting increased analgesic intake by women with endometriosis during the COVID-19 pandemic. (2) Methods: The increased intake of over-the-counter (OTC) and prescription-only (PO) analgesics was assessed with an anonymous online questionnaire, along with demographic, pandemic-specific, disease-specific, and mental health characteristics. Anxiety and depression were assessed with the Generalized Anxiety Disorder Scale (GAD-2) and the Patient Health Questionnaire for Depression (PHQ-2), respectively. Pain-induced disability was assessed with the pain-induced disability index (PDI). (3) Results: A high educational level (OR 2.719; 95% CI 1.137-6.501; = 0.025) and being at higher risk for depressive disorders, as measured by PHQ-2 ≥ 3 (OR 2.398; 95% CI 1.055-5.450; = 0.037), were independent risk factors for an increased intake of OTC analgesics. Current global pain-induced disability (OR 1.030; 95% CI 1.007-1.054; = 0.010) was identified as a risk factor for an increased intake of PO pain medication. The degree of reduction in social support and in social networks were independent predictors of an increased intake of PO analgesics in a univariate logistic regression analysis, but lost significance when adjusted for additional possible influencing factors. (4) Conclusions: In this population, an increased intake of OTC analgesics was related to a higher educational level and having a depressive disorder, while a higher pain-induced disability was an independent risk factor for an increased intake of PO analgesics. Pandemic-specific factors did not significantly and independently influence an increased intake of analgesics in women with endometriosis during the first wave of the COVID-19 pandemic in Germany. Healthcare providers should be aware of the possible factors related to increased analgesic use in women with endometriosis in order to identify persons at risk for the misuse of pain medication and to prevent potential adverse effects.