The 26-year-old forward signed a one-year $2.25 million contract with Toronto on July 17 and can be an unrestricted free agent at the end of this season.
Engvall has 21 points (12 goals, nine assists) in 58 games.
Selected by Toronto in the seventh round (No. 188) of the 2014 NHL Draft, Engvall has 83 points (42 goals, 41 assists) in 226 regular-season games and four assists in 17 Stanley Cup Playoff games.
RELATED: [2022-23 NHL Trade Tracker]
The Islanders (31-25-7), who are the first wild card into the Stanley Cup Playoffs from the Eastern Conference, also acquired center Bo Horvat from the Vancouver Canucks on Jan. 30.
The Maple Leafs (37-15-8), who are second in the Atlantic Division, 15 points behind the first-place Boston Bruins and four points ahead of the third-place Tampa Bay Lightning, also acquired defenseman
Luke Schenn
from the Vancouver Canucks, and defenseman Erik Gustafsson and a first-round pick in the 2023 NHL Draft for defenseman Rasmus Sandin on Tuesday.
Toronto acquired defenseman Jake McCabe and forward Sam Lafferty from the Chicago Blackhawks on Monday, and forwards Ryan O'Reilly and Noel Acciari in a three-team trade with the St. Louis Blues on Feb. 17.
