Making a complete list is surprisingly difficult, considering that this information is probably known locally. Below is an incomplete list by country.
If you can add to the list, please use the answer function to write the woman’s name and country.
Canada: Jennie Trout/Emily Stowe
Colombia: Anna Galvis Hotz
Ecuador: Matilde Hidalgo de Procel
Germany: Dorothea Erxleben
France: Madeleine Brès, but pre-modern women such as Magistra Hersend also practiced medicine.
Korea: Jang Geum
Peru: Laura Rodriguez Dulanto
Philippines: Honoria Acosta-Sison
Russia: Nadezhda Suslova
Sweden: Lovisa Årberg
UK: Elizabeth Garrett Anderson
USA: Elizabeth Blackwell
Suggestions welcome, just keep in mind this is a history blog so dead women are strongly preferred.
You can see all the medieval posts here.
And all the Draw a Cool Chick from History posts here.