Structural inequalities persist in society, conferring systematic advantages to some people at the expense of others, for example, by giving them substantially more influence and opportunities. Using bibliometric data about authors of scientific publications, we identify two types of structural inequalities in scientific citations. First, female authors, who represent a minority of researchers, receive less recognition for their work (through citations) relative to male authors; second, authors affiliated with top-ranked institutions, who are also a minority, receive substantially more recognition compared to other authors. We present a model for the growth of directed citation networks and show that citations disparities arise from individual preferences to cite authors from the same group (homophily), highly cited or active authors (preferential attachment), as well as the size of the group and how frequently new authors join. We analyze the model and show that its predictions align well with real-world observations. Our theoretical and empirical analysis also suggests potential strategies to mitigate structural inequalities in science. In particular, we find that merely increasing the minority group size does little to narrow the disparities. Instead, reducing the homophily of each group, frequently adding new authors to a research field while providing them an accessible platform among existing, established authors, together with balanced group sizes can have the largest impact on reducing inequality. Our work highlights additional complexities of mitigating structural disparities stemming from asymmetric relations (e.g., directed citations) compared to symmetric relations (e.g., collaborations).