Will the vaccine cause infertility?

No, there is no evidence to suggest the vaccine will have any impact on fertility. The Pfizer-BioNTech and Moderna COVID-19 vaccines are mRNA vaccines which cause your immune system to make antibodies against a protein found in the SARS-CoV-2 virus (see section How do the Pfizer-BioNTech and Moderna vaccines work?

Concerns have been circulating on social media about a placental protein sharing a gene sequence with the protein that the vaccine helps you make antibodies against. Antibody binding is complex, and it would be extremely unlikely that antibodies you make from the vaccine would bind to a placental protein just based on one shared sequence. If this did happen, it would also be expected with natural infection as well (since the vaccine helps you make the same antibodies as you would in natural infection) and this has not been observed.