Background Ethiopia is currently planning to introduce Social Health Insurance (SHI) that will lead to universal health coverage and assist a country to achieve its health system’s objectives and to prevent the catastrophic health expenditure. But there is no evidence until now about the level of acceptance of the proposed SHI among government-owned companies’ employees. Therefore, this study was intended to assess the acceptance of SHI and associated factors among government-owned companies’ employees in northwest Ethiopia. Methods An institution-based cross-sectional study was conducted from February 1 to April 30, 2019. A randomly selected 541 government-owned companies’ employees were participated in the study. A pretested self-administered structured questionnaire was used that consisted sociodemographic and economic, health status-related factors, attitude (measured by 12 items), organizational related factors and knowledge about SHI (measured by 11 items). Finally, binary logistic regression analysis was performed and in the multivariable logistic regression analysis, a significant level at a p-value of < 0.05 and Adjusted Odds Ratio (AOR) with 95% confidence interval (CI) were used to identify factors statistically associated with SHI acceptance. Results Overall, 32% (95% CI: 27.7–36.2) of the government-owned companies’ employees accepted the proposed Ethiopian SHI scheme. Self-perceived health status (AOR: 8.55, 95% CI: 2.69–27.13), heard about SHI (AOR: 1.69, 95% CI: 1.12–2.54), coverage of medical healthcare cost (AOR: 0.60, 95% CI: 0.39–0.92), work experience (AOR: 0.49, 95% CI: 0.26–0.89) and quality of healthcare service at the facilities (AOR: 0.17, 95% CI: 0.04–0.71) were significantly associated with acceptance of SHI among government-owned companies’ employees. Conclusions One-third of the study participants accepted the proposed Ethiopian SHI scheme. Self-perceived health status, quality of healthcare service at health facilities, coverage of the medical cost by their organization, heard about SHI and work experience were the factors that affect acceptance of the proposed SHI among the government-owned company employees. Therefore, policymakers should devise a plan to promote the benefit packages of SHI for the formal sector employees to start the implementation.