He started his professional career in Ilves in 1988-89 and played until 2001, representing also TPS, Ässät and Kärpät in the SM-liiga. His playing career also included one season in Sweden with AIK. Highlights were reaching the Liiga finals with Ilves in 1990 and earning promotion to Finland's top-tier with Kärpät in 2000.
After his playing career, Kivi started his coaching career as an assistant coach at Liiga club Ässät. In 2011, he was promoted to the head coaching job and led Ässät to the Finnish championship in 2013, while receiving Coach of the Year honors. After this successful season, he joined the coaching staff of the Finnish ice hockey federation and coached Finland's men's national junior ice hockey team to the title at the World Junior Championship in 2014.
Prior to the 2014-15 season, Kivi accepted the job as head coach of Traktor Chelyabinsk of the Kontinental Hockey League (KHL). He was relieved of his duties in October 2014. Kivi was named head coach of Finnish Liiga side Ilves prior to the 2016-17 campaign.
- Laine, Sami (April 24, 2013). "Ässien sankariluotsi: "Pori tarvitsi tätä!"". YLE. Retrieved January 5, 2014.
- Palomäki, Ilkka (April 5, 2013). "Yle Urheilu antoi kouluarvosanat - tässä on Suomen maailmanmestarijoukkue!". YLE.
- "Jortikka replaces Kivi". www.iihf.com. Retrieved 2016-05-29.
- "Karri Kivi: Traktor is in heart of Chelyabinsk fans, and I hope it will stay the same". ХК Трактор (in Russian). Retrieved 2016-05-29.
- "Karri Kivi Ilveksen päävalmentajaksi kausiksi 2016-18". liiga.fi. Retrieved 2016-05-29.
- Biographical information and career statistics from Eliteprospects.com, or Eurohockey.com, or The Internet Hockey Database
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