Anna Stieblich was born in Bremen on February 20, 1965. From 1986 to 1990 she trained as an actress at the Hochschule für Musik und Theater in Hanover, followed by engagements at the Stadttheater Luzern (1990/91) and the Hessisches Staatstheater Wiesbaden (1992/93). At the same time, she attended seminars on voice training at the Roy Hart Theatre in Thoiras, southern France (1990-92).   

After numerous further theater engagements, including at the Theater Basel and the Staatstheater Dresden, Stieblich increasingly took on smaller television roles in the early 2000s. She made her feature film debut in 2005 with a supporting role as a registrar in the award-winning relationship story "KussKuss". She played a larger supporting role in Didi Danquart's comedy "Offset" (2006).   

Anna Stieblich became known to a larger audience through the role of Doris in the successful pre-watershed series "Türkisch für Anfänger" ("Turkish for Beginners", 2006-2008). In 2009, she landed a permanent role as a forensic doctor in the crime series "SOKO Leipzig." In addition, Stieblich was seen in television dramas as well as in guest roles in other series. She had supporting roles on the big screen as the mother of the young main character in "Mein Freund aus Faro" ("My Friend from Faro", 2008) and as a school secretary in the historical soccer film "Der ganz große Traum" ("Lessons of a Dream", 2011).

She played a leading role directed by Didi Danquart in the drama "Bittere Kirschen" ("The Path to the Past", 2011), as an actress who embarks on a journey into her family's past after the death of her mother. In 2012, she reprised the role of Doris for the feature film "Türkisch für Anfänger" ("Turkish for Beginners"), based on the TV series. In the next few years, Stieblich was seen more and more often on the big screen. She was the mother of the main female character in "Schoßgebete" ("Lap Prayers", 2014), a mother in the Jewish coming-of-age story "Simon sagt auf Wiedersehen zu seiner Vorhaut" ("Time to Say Goodbye", 2015) and a pilgrim in "Ich bin dann mal weg" ("I'm Off Then", 2015).

On television, she played leading roles in the mother-daughter story "Meine Mutter, meine Männer" (2014) and the culture-clash comedy "Der Hodscha und die Piepenkötter" (2016). She also was a regular in the series "Phoenixsee" (2016), "Die Mockridges - Eine Knallerfamilie" (2016) and "Gipfelstürmer - Das Berginternat" (2019). In "SOKO Leipzig" she continued to embody the forensic doctor Sabine Rossi. In 2021, "Die Vergesslichkeit der Eichhörnchen" was released in cinemas, with Stieblich as the bossy, controlling daughter of a senior citizen in need of care.   

Anna Stieblich is married to director Didi Danquart.