Schmid, who won two MLS Cups during his career, stepped down from his role as Galaxy coach earlier this year.
His passing, due to a "personal health matter", was confirmed in a statement from his family on Wednesday.
In a separate statement, MLS commissioner Don Garber paid tribute to Schmid.
"Major League Soccer is devastated by the news of the passing of Sigi Schmid," he said.
"Sigi will go down as one of the leading figures in the history of our league. From Los Angeles to Columbus and Seattle, Sigi won more games than any coach in MLS history and led his clubs to multiple championships, including two MLS Cups and five Lamar Hunt U.S. Open Cups.
"Sigi's passion for soccer was unrivalled, and he was loved and admired by everyone in MLS.
"We deeply mourn his passing and send our heartfelt condolences to his wife Valerie, their children, and all of his loved ones."
Schmid won the MLS Cup with the Galaxy in 2002 before leading the Columbus Crew to the title six years later.
He guided the Seattle Sounders to the MLS Supporters' Shield in 2014 before returning to the Galaxy three years later.
A two-time MLS Coach of the Year, Schmid compiled 240 regular-season wins – the most of any coach – and 26 post-season victories.
Schmid is survived by his wife Valerie and four children – Erik, Lacey, Kurt and Kyle.