Considering the key role that companies must play to achieve the Sustainable Development Goals (SDGs), this paper aims to analyze the effect of the presence of two types of institutional investors (governments and pension funds) in large companies' ownership structure on the alignment of their sustainability strategy towards the 2030 Agenda as well as the moderating effect that firm internationalization and industry's sensitivity to stakeholder pressures have on the influence of these two institutional investors on business commitment to the SDGs. For a sample of 4089 multinational companies from 2015 to 2018, the results show that institutional ownership does matter for business commitment to the SDGs, but in a different way depending on the type of investor. Specifically, ownership by government favors commitment to the SDGs, while ownership by pension funds has a negative impact, which is partially corrected in the case of globalized companies as well as in those firms belonging to industries, which are highly sensitive to stakeholder pressures. These findings seem to suggest that institutional investors' support the implementation of the SDGs by the companies in which they invest is mainly driven by corporate complexity.