Chychrun was knocked into the boards by Bruins defenceman Derek Forbort early into the second period. The 23-year-old Chychrun headed to the dressing room and did not return.
Chychrun has 27 points (seven goals and 14 assists) in 47 games this season and has been linked to trade rumours with the deadline just a little over a week away.
Arizona erased a two-goal deficit but fell 3-2 to Boston, snapping a season-high four-game winning streak.
The Coyotes are last in the Western Conference with an 18-36-4 record and continue their road trip Monday visiting the Ottawa Senators.