Now a study has found babies born to these women have differences in their brains which may make them more susceptible to anxiety disorders in later life.
This could be because serotonin, the so-called "happy hormone", affects the development of the child’s brain in the womb. Antidepressants called selective serotonin reuptake inhibitors (SSRIs) are believed to increase levels of the hormone.
Led by Dr Claudia Lugo-Candelas at Columbia University, New York, the study of 98 babies looked at those born to women without depression; women with depression but not on pills; and women on SSRIs.
The researchers found babies born to women on these drugs had a larger amygdala and insular cortex - areas of the brain "critical to emotional processing".
Professor Andrew Whitelaw, of the University of Bristol, who was not involved in the research, said: "These regions of the brain are involved in the regulation of fear and anxiety. Other studies have shown that enlargement and activity in these regions are associated with anxiety disorders.
"However, infants in this study were examined at just a few weeks of age and the findings may be transient."
Research from Finland has previously found children of women on SSRI pills in pregnancy are more likely to develop depression as teenagers.
The Columbia study showed babies whose mothers had taken these antidepressants while pregnant had more grey matter in their amygdala and insular cortex than those whose mothers were not depressed or depressed but not on pills.
MRI scans taken when they were three-and-a-half weeks old also showed greater connection between the two areas. This may affect how they process fear and whether they feel anxious in uncertain situations.