Poverty and inadequate housing for refugees in Scotland also puts health at risk, the British Red Cross said.
Research and interviews with asylum seekers found reports of infested flats and delays to payments that left some pregnant women unable to travel to hospital appointments and new mothers struggling to buy essentials.
It also found several women have considered or attempted suicide during their time in Scotland.
The study - A Healthy Start? - carried out by the University of Strathclyde’s Centre for Health Policy and commissioned by the Red Cross looked into the challenges pregnant women in Scotland face during their time seeking refugee protection.
Researchers interviewed pregnant and post-natal women in the asylum system living in Glasgow, along with service providers.
The British Red Cross wants “adequate and consistent support” for all pregnant women and is calling for greater clarity around the responsibility of local authorities to provide support to pregnant women at risk of destitution.
Phil Arnold, head of refugee support Scotland for the British Red Cross, said: “All women need support during pregnancy no matter what their immigration status.
“All women need a safe, secure place to live, nutritious food, proper rest and to be able to access good quality healthcare throughout their pregnancy. For women seeking refugee protection, these essentials are often out of reach.
“Homelessness and destitution during pregnancy is unacceptable in 21st-century Britain.
“The Home Office must provide adequate support to all pregnant women regardless of their immigration status.
“They must also urgently make sure that their accommodation providers are housing women and children in suitable and secure properties.”