Hruša was born in Brno, Czech Republic, on July 23, 1981. He played the piano in his youth and also became proficient on the trombone. He eventually developed an interest in conducting and enrolled at the Prague Academy of Performing Arts, where he studied conducting with Jirí Belohlávek, Leoš Svárovský, and Radomil Eliska. Hruša played both the trombone and piano in the student orchestra there and graduated in 2004. By that time, he had already held the post of associate conductor with the Czech Philharmonic Orchestra for two years. He concluded his service with the Czech Philharmonic in 2005 and that same year took on a trio of assignments: associate conductor of the Orchestre Philharmonique de Radio France, chief conductor of the Bohuslav Martinu Philharmonic in Zlín, Czech Republic, and principal guest conductor of the Prague Philharmonia. Hruša held his posts in France and Zlín until 2006, the year he signed the recording contract with Supraphon. The deal called for six recordings, and the first two of them appeared in 2006, the latter containing Dvorák's Suite in A and Suk's Serenade for strings and Fantastic Scherzo, all with the Prague Philharmonia.
Hruša found critical success with the Prague Philharmonia and in 2008 became principal conductor of the ensemble. That same year, he conducted acclaimed performances of Bizet's Carmen at both the Glyndebourne Festival and with Glyndebourne on Tour. He also led a performance of Massenet's Werther at Opera Hong Kong. Hruša debuted in the U.S. in 2009, leading concerts with the Milwaukee and Indianapolis Symphony Orchestras. From 2010 until 2012, Hruša served as the music director of Glyndebourne on Tour. In 2011, Hruša led an acclaimed performance of Britten's The Turn of the Screw at the Glyndebourne Festival. Later that year, Hruša was named the music director at the Royal Danish Opera, effective in 2013, but in early 2012, he resigned the post owing to announced budget cuts.
Hruša remained in his post with the Prague Philharmonia until 2015, after which he made significant debuts at La Scala, the Vienna State Opera, and the Frankfurt Opera in the 2015-2016 season and was named the principal guest conductor of the Czech Philharmonic. The following season, Hruša became the chief conductor of the Bamberg Symphony Orchestra. In 2018, he became one of the Philharmonia Orchestra's principal guest conductors. Hruša, leading the Bavarian Radio Symphony Orchestra, backed violinist Augustin Hadelich in a recording of Dvorák's Violin Concerto in A minor, Op. 53, on the album Bohemian Tales in 2020, which earned Hruša a Grammy nomination. In 2021, he became the principal guest conductor of the Orchestra dell'Accademia Nazionale di Santa Cecilia and issued a recording of Mahler's Fourth Symphony with the Bamberg Symphony on the Accentus label. ~ Robert Cummings & Keith Finke, Rovi