The aims of this paper are (1) to assess the role of sociodemographic and psychosocial risk factors on antenatal anxiety (AA) and antenatal depression (AD) in first-generation migrant women in Geneva, as compared to a control group of native Swiss women, and (2) to examine the role of acculturation and other sociocultural factors in the development of antenatal distress in migrant women. A sample of 43 migrant and 41 Swiss pregnant women were recruited during the third trimester of pregnancy. AA was assessed by using the State Trait Anxiety Inventory, and AD by using the Edinburgh Postnatal Depression Scale. Acculturation was assessed as a bidimensional process comprising attachment to the heritage culture and adaptation to the local Swiss culture, using the Vancouver Index of Acculturation. AA in migrant women was mainly predicted by psychosocial factors, namely socioeconomic status, marital support, family presence in Geneva and parity, while AD was predicted by one dimension of acculturation, i.e., attachment to the heritage culture. Our study can inform perinatal health care professionals about some specific risk factors for antenatal distress in migrant women in order to increase systematic screening procedures.