Peri Baumeister was born in Berlin in 1986. From 2007 to 2011, the sister of actress Muriel Baumeister studied at the August Everding theatre academy in Munich, and during that time, she already appeared in stage adaptations of Lars von Trier's "Dogville" and "Manderlay" at the Metropol theatre.

She made her screen debut as the impulsive and obsessive sister of poet Georg Trakl in the drama "Tabu – Es ist die Seele ein Fremdes auf Erden" ("Tabu: The Soul Is a Stranger on Earth", 2011). For her performance, she was named Best Actress at the Max-Ophüls-Preis film festival. This was followed by a leading role in Oliver Ziegenbalg's "Russendisko" ("Russian Disco", 2012), which was eventually released before "Tabu".

In 2013, Baumeister got a minor part as the duchess Elisabeth von Plettenberg in "Ein weites Herz – Schicksalsjahre einer deutschen Familie" (2013, TV), a filmic biography about Isa Vermehrens and she played a nurse in "Feuchtgebiete" ("Wetlands", 2013), based on the same-titled bestselling novel. She received a nomination for "Best actress in a supporting role" for her portrayal of a trainee who begins an affair with her boss (Matthias Brandt) in Hermine Huntgeburth's "Männertreu" (2014, TV). Perimeister proofs her comedic talent in "Irre sind männlich" (2014) in which she plays the love interest of two self-proclaimed womanizers.

In the Norwegian television series "Kampen om tungtvannet" ("The Saboteurs", 2015) about Hitler's attempts to build an atomic bomb, Perimeister plays the wife of the famous physicist Werner Heisenberg. Also in 2015, the actress got a leading role as the half-arabic fiancée of a jewish man in the multicultural comedy "Herbe Mischung" ("A Bitter Mix", 2015). In "Oregon Pine", she played the love interest of an engineer. The film premiered at the Filmfestival Achtung Berlin in 2016. Perimeister got a leading role in "Unsere Zeit ist jetzt" ("Cro: Don't Believe the Hype", 2016) where she plays one of three filmmakers who want to make film about the Hip Hop Star Cro.

In 2017, she appeared in the second season of the Viking series "The Last Kingdom" in a leading role as the sister of a Viking king, followed by parts as the mother of the title character in the children's film "Liliane Susewind - Ein tierisches Abenteuer" ("Little Miss Doolittle", DE/FR/BE 2018) and as the writer Elisabeth Hauptmann in "Mackie Messer - Brecht's Dreigroschenfilm" ("Mack the Knife – Brecht's Threepenny Film", DE/BE 2018). Lars Kraume cast her as Ise Gropius in the series "Die Neue Zeit" ("Bauhaus – A New Era", 2019), and she played a policewoman in the gangster series "Skylines" (2019).  

Baumeister played other leading roles as the mentor of a crystal meth addict in "9 Tage wach" (2020, TV), as a "good" vampire in the horror thriller "Blood Red Sky" (2021) and as the manager of a vain movie star in the comedy "Liebesdings" ("Love Thing", 2021).