Canellakis grew up in New York in a musical family: her mother was a pianist, her father was a conductor, and her brother Nicholas is a cellist. Karina took up the violin as a child, attending the Curtis Institute in Philadelphia, where she studied violin and conducting and graduated in 2004. She earned a spot as a substitute with the Chicago Symphony Orchestra, where she was influenced and inspired by Bernard Haitink and Pierre Boulez. From 2005 to 2007, Canellakis was a member of the Berlin Philharmonic Orchester-Akademie, performing under Sir Simon Rattle, who encouraged Canellakis to commit and fully pursue a career as a conductor. She continued to perform with the Chicago Symphony, including her first BBC Proms performance as a second violinist in 2008 for Mahler's Symphony No. 6, under Haitink. From 2011 until 2013, she studied conducting with Alan Gilbert at the Juilliard School.
Canellakis' first conducting post came as the assistant conductor with the Dallas Symphony Orchestra from 2014 until 2016. An early performance with this group was in the fall of 2014, when she conducted Shostakovich's Symphony No. 8, without rehearsal, as a last-minute substitute for Jaap van Zweden. The following year, she similarly made her European conducting debut as an emergency substitute for Nikolaus Harnoncourt, leading the Chamber Orchestra of Europe. In 2016, Canellakis won the Georg Solti Conducting Award, and she premiered David Lang's chamber opera, the loser, with baritone Rod Gilfry and the Bang on a Can Opera Orchestra. Canellakis' interest in contemporary music has also allowed her to work with the International Contemporary Ensemble. These accomplishments led to guest conducting spots with orchestras throughout Europe and North America, even extending to Australia and Hong Kong. In 2017, Canellakis made her return to the Proms, this time as a conductor, leading the BBC Symphony Orchestra, and she made her debut with the Berlin Radio Symphony Orchestra.
2018 was a pivotal year for Canellakis: she debuted as a guest conductor with the Netherlands Radio Philharmonic Orchestra and the London Philharmonic Orchestra, and she became the first woman to conduct the Nobel Prize concert. In 2019, Canellakis took up the post of chief conductor with the Netherlands Radio Philharmonic and became the first woman to conduct the First Night of the Proms. This concert featured the premiere of Zosha Di Castri's Long Is the Journey, Short Is the Memory, marking the 50th anniversary of the Apollo 11 moon landing, as well as Dvorák's The Golden Spinning Wheel and Janácek's Glagolitic Mass. That year, she was named the principal guest conductor of the Berlin Radio Symphony, taking up the same role with the London Philharmonic in 2020. Canellakis has also explored operatic works, including Janácek's Kat'a Kabánova, Tchaikovsky's Eugene Onegin, and several Mozart operas. ~ Keith Finke, Rovi