Asnicar was born in Buenos Aires, Argentina, the daughter of Gustavo Asnicar and Adriana Mendoza. Asnicar has stated that she is also of Italian and Slovenian ancestry. She has one brother, Iván, and her religion is Roman Catholicism. During her childhood Brenda studied at the Italian Cultural Centre school in Villa Adelina, where she learned to speak fluent Italian.
Asnícar made her television debut on the children's program Cantaniño in 1999, when she was 8 years old. In 2003 at age 12 she began working on the TV show Chicos Argentinos.
Asnícar debuted as a singer on albums for Cataniño and Chicos Argentinos. These albums were a commercial success in Argentina and numerous other countries, most notably Italy.
In 2007, Asnícar landed her first leading role on television, as Antonella Lamas in Patito feo (Ugly Duckling), also created by Marcelo Tinelli and produced by Ideas del Sur. It became one of the most popular adolescent television programs in Argentina, Latin America, Israel and Portugal. The series lasted from 2007 to 2008 and held high viewer ratings and earning four Martín Fierro Awards for Best Juvenile Program.
From 2007 to 2009, Patito feo released six studio albums, of which five were certified platinum and one was certified gold by the Argentine Chamber of Phonograms and Videograms Producers. Patito feo won a Premios Carlos Gardel and three nominations for Carlos Gardel Awards.
From 2009 to 2011, Asnícar starred in the series Sueña conmigo. The series earned high ratings and was a huge success in Latin America, Spain, and Italy. In 2011, the cast toured Argentina, Latin America, and Italy, performing songs from the series.
In 2011 she starred in the series Los únicos with María Eugenia Suárez and Nicolás Cabré in El Trece and under production of Pol-ka.
Since January 2012, Asnicar had starred the Telemundo series Corazón valiente (Fearless Heart), along with Adriana Fonseca, Ximena Duque, José Luis Reséndez and Fabián Ríos, as Fabiola Arroyo, one of its leading characters.
In 2016, Asnicar previewed The B Collection with mcma London; the collection launched in February 10, 2016.
From 2013 2015, Asnícar landed the role of Juana Carbajal series Cumbia Ninja, which achieved international success. She also became a member of successful music group Cumbia Ninja in the series, along with Ricardo Abarca.
In 2016, Asnicar starred on Por amarte así, a new television series by Claudio Lacelli, opposite Gastón Soffritti, Catherine Fulop and Facundo Gambandé.