Teräväinen has a younger brother and sister. His father is a dentist. His brother Eero is a defenceman with HIFK of the Liiga, and previously played with the Lincoln Stars of the United States Hockey League (USHL) and with the Finland men's national under-18 ice hockey team at the 2017 IIHF World U18 Championships. His sister, Satu, appeared at the 2019 IIHF Women's World U18 Championship with the Finnish women's national under-18 ice hockey team and played with Kiekko-Espoo of the Naisten Liiga, the premier women's ice hockey league in Finland, most recently during the 2019–20 season.