The move gives Asplund, 22, an opportunity to play while he waits for the 2020-21 North American season to begin. He can return to the Sabres whenever training camp opens.
The COVID-19 pandemic has forced the NHL and AHL to target early December as a possible start date instead of October.
Asplund played his first 29 NHL games in 2019-20, compiling one goal and three points. He also played 33 contests with the Rochester Americans, scoring three goals and 19 points.
The Sabres selected Asplund in the second round in 2016, 33rd overall. He joined the Amerks in 2018 after playing four seasons with Farjestads BK Karlstad, a Swedish Hockey League team.