The deal was announced by Sabres general manager Darcy Regier on Monday, and reached shortly before the NHL trade deadline.
Hodgson was the selected 10th overall in the 2008 draft and is playing his first full NHL season. Kassian is a physical forward, whom the Sabres selected 13th overall in the 2009 draft.
In a separate deal, Buffalo traded center Paul Gaustad to Nashville for a first-round draft pick this year. The Predators also acquired Buffalo's fourth-round pick in next year's draft.