Kloetzel was born in 1968 and grew up near Baltimore, Maryland. She took up the cello at age six. Kloetzel attended the Juilliard School, where she won the institution's top award, the Peter Mennin Prize for Outstanding Leadership and Achievement in Music. Her teachers along the way included Aldo Parisot, William Pleeth, and Paula (Virizlay) Skolnick, and she had chamber music training with members of the Juilliard String Quartet, the Amadeus Quartet, and the Cleveland Quartet. Kloetzel performed with pianist André Previn at the La Jolla Chamber Music Festival, and Previn invited her to the Caramoor Summer Music Festival in upstate New York to appear as a Rising Star.
In 1994, Kloetzel made her recording debut on the album Inhabit My Heart by the pop-folk group GrooveLily. Her classical debut came in 1996 on the album Arsenal of Democracy by composer Julia Wolfe. That year, Kloetzel co-founded the Cypress String Quartet in San Francisco, remaining its cellist until it disbanded in 2016. Including recordings by that group, she has issued more than 35 albums. As a soloist, Kloetzel has performed at such prestigious venues in the U.S. and abroad as Lincoln Center in New York, Washington's Kennedy Center for the Performing Arts, and the Ravinia Festival in suburban Chicago. She has often appeared at colleges and music conservatories internationally. Kloetzel is a champion of new music and has premiered more than 50 works, including several concertos as well as a cello sonata by Joseph Landers, written for her specifically. She has given several premieres of works by Elena Ruehr. She received the Copland Award, marking her performances of works by living American composers. In 2016, Kloetzel joined the faculty at the University of California at Santa Barbara, where she is professor of cello, head of performance, and head of strings. The Cypress String Quartet recorded a complete cycle of Beethoven's quartets for the Avie label, and in 2022, she returned to Beethoven and to that label with an album of Beethoven's complete works for cello and piano, with pianist Robert Koenig. ~ James Manheim, Rovi