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.