The new deal is worth $7.8 million with an average annual value of $2.6 million, according to media reports.
The 22-year-old Kase set career highs in goals (20), assists (18), points (38) and plus-minus (plus-18) last season. He also had five game-winning goals.
"Ondrej is a skilled player that has a bright future in this league," Ducks general manager Bob Murray said. "He can skate and score and will continue to improve as a player as he gains more experience."
Kase, the only player selected in the seventh round of the 2014 draft to have reached the NHL, also has represented the Czech Republic in the world junior championships in 2014 and '15.