I am looking for great books by Finnish authors who identify as female. I'm looking for a diverse range of books: from fiction to non-fiction; books written a…

This is of course a question where the method of defining who is significant can vary. There are a lot of book and authors, but i start here with a few and hope that my colleagues will continue the list. 

The first name that comes in mind is Minna Canth who lived 1844-1897 and was a very significant female writer and a champion of equal rights, https://kansallisbiografia.fi/english/person/2816
The translations of her work can be hard to find, but here are three that I found in one of our former answers:
Sanoi Minna Canth - Pioneer Reformer, Extracts from Minna Canth's Works and letters. Edited by Ritva Heikkilä. Porvoo 1987. Sivut 141-280.
Anna-Liisa. Portraits Of Courage. Plays by Finnish Women. Edited by S. E. Wilmer. Helsinki1997.
The Worker's Wife, English lanquage adaption by Mary Taanila Lehtinen and David Hanhilammi. English Language Premiere July 2, 1980 Minnesota University.

In a site that lists a few classics of finnish literature there are two other women too, http://kaino.kotus.fi/korpus/klassikot/meta/klassikot_coll_rdf.xml

Aino Kallas 1878 – 1956 who was a very international figure and a known person in finnish cultural life. Her most known work Suden morsian The Wolf’s bride, https://www.worldcat.org/title/three-novels/oclc/58501601&referer=brief…

Edith Södergran 1892 – 1923 who was a finnish-swedish poet and wrote in Swedish. It looks like her poetry isn’t translated elsewhere except in texts that are with musical recordings, https://www.worldcat.org/title/framtidens-skugga-landet-som-icke-ar/ocl…

National Biography of Finland lists only twelve finnish writers in English, but four of them are women, Canth is there of course, these following two are feminists, writers, and active persons in the society Friberg, Maikki (1861 - 1927) https://kansallisbiografia.fi/english/person/3315 Gripenberg, Aleksandra (1857 - 1913), https://kansallisbiografia.fi/english/person/4437

The fourth is Tove Jansson (1914 - 2001), who has written the widely internationally popular Moomin-books. They have been translated in many languages, https://kansallisbiografia.fi/english/person/1395

More recent writers can be found in English translations, here one selection, http://www.kiiltomato.net/suomen-kirjallisuus-norjalaisten-silmin/

Leena Krohn, Anja Snellman, Kari Hotakainen, Monika Fagerholm, Leena Lander, Märta Tikkanen and Rakel Liehu.

You can check the translations in either worldcat.org or http://dbgw.finlit.fi/kaannokset/index.php?lang=ENG

In the anthology Female voices of the North : an anthology. 2 Olsen, Inger ; Rossel, Sven H. ; Wenusch, Monica Praesens Verlag 2006., https://www.finna.fi/Record/arto.1487035#componentparts there are also Eeva-Liisa Manner and Rosa Liksom mentioned in addition to the previously mentioned and Inger-Mari Aikio-Arianiaick from Northern Finland. 

In a reading list, which can be found in Kirjasampo, a finnish literature site, there are for ex. Anna-Leena Härkönen and Eve Hietamies. https://www.kirjasampo.fi/fi/node/1742

Kaari Utrio is a writer who has written both fiction and historical studies, https://kaariutrio.fi/wp/

A known academic writer Päivi Setälä wrote also about history and female history, https://www.worldcat.org/search?q=au%3Ap%C3%A4ivi+set%C3%A4l%C3%A4&fq=ln%3Aeng&qt=advanced&dblist=638

But perhaps the author that has gained most international interest and fame recently is of Sofi Oksanen. https://www.worldcat.org/search?q=sofi+oksanen&qt=results_page Her novel Purge was a huge success and has been translated and read all over the world https://www.worldcat.org/title/purge/oclc/1042156580&referer=brief_results.

Many writers haven’t been mentioned here, but there are a lot female writers to recommend Orvokki Autio, Anni Blomqvist, Kaarina Helakisa, Laila Hirvisaari, Helvi Hämäläinen, Eeva Joenpelto, Maria Jotuni, Anu Kaipainen, Eeva Kilpi, Kirsi Kunnas, Ulla-Lena Lundberg, L. Onerva, Anni Polva, Aino Räsänen, Elvi Sinervo, Anni Swan, Aale Tynni, Tyyni Tuulio, Marja-Liisa Vartio. Here is the link to a name list in the National Biography in Finnish, https://kansallisbiografia.fi/kansallisbiografia?professions=kirjailija…