Fleury is in the first season of a two-year contract he signed with the Hurricanes on Oct. 27 and can become a restricted free agent after next season.
The 24-year-old defenseman has scored one goal in 35 games this season.
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Selected by Carolina with the No. 7 pick in the 2014 NHL Draft, Fleury has scored 24 points (five goals, 19 assists) in 167 regular-season games and two goals in 17 Stanley Cup Playoff games.
"He's a young defenseman, big kid, skates very well, always has," Ducks general manager Bob Murray said. "He's kind of been stuck in Carolina a little bit, behind a really good, solid defense, hasn't been given a real good opportunity. I think this is a great opportunity for him and for us."
Hakanpaa has one assist in 42 games this season and can become an unrestricted free agent after the season.
Selected in the fourth round (No. 104) by the St. Louis Blues in the 2010 NHL Draft, the 29-year-old has scored two points (one goal, one assist) in 47 NHL games.
"Jani is a big, physical defenseman," Hurricanes general manager Don Waddell said. "As a right shot he will be an ideal partner for an offensive-minded, left-handed blueliner."
The Hurricanes (27-9-4) are tied with the Tampa Bay Lightning for first in the eight-team Discover Central Division. The top four teams in each of the four divisions will make the playoffs.
The Ducks (12-23-7) are last in the eight-team Honda West Division, 13 points behind the fourth-place St. Louis Blues.
NHL.com independent correspondent Dan Arritt contributed to this report
