The role of sustainable development in the export intensity of small and medium-size enterprises (SMEs) represents an open research question. We consider sustainable development through the environmental, social, and governance (ESG) dimensions as well as via firms’ innovative activity indicators. Our objective is to reveal the sustainability determinants of export intensity of SMEs in emerging markets subject to financial constraints, which is one of the major obstacles for SMEs. Our sample is based on the 2018–2020 Business Environment Enterprise Performance Survey data. The Heckman model allows us to reveal the factors relevant for SMEs to gain access to foreign markets under the control of financial constraints specific for SMEs. We also analyze the determinants of the SMEs’ share of direct exports in revenue. Our results demonstrate that innovative activity and corporate social responsibility facilitate entry to foreign markets, while equity concentration is a major deterrent. In particular, we reveal a significant positive effect of research and development investment on export intensity. Our findings highlight the complex nature of the interrelations between the SMEs’ share of direct exports in revenue and ESG consciousness. We find that other significant factors are political links of the top management, the gender composition of production and administrative units, employee training facilities, and ownership structure.