The 23-year-old midfielder was hurt midway through Wednesday's training session, with scans confirming damage to an anterior cruciate ligament.
"We're all extremely disappointed for Bailey and empathise with him greatly," Bulldogs football director Chris Grant said.
"The entire club will rally around him during this difficult time as he begins his rehab journey."
Smith is out of contract at the end of 2024 and has been the subject of speculation about a move away from the Bulldogs.
Hawthorn and Geelong have been most strongly linked to the midfielder, who endured a tough run of form midway through 2023.
It sparked fierce external criticism and a strong defence from Bulldogs coach Luke Beveridge.
Smith had struggled to break into a star-studded midfield boasting prolific ball-winners Marcus Bontempelli, Tom Liberatore, Adam Treloar and Jack Macrae.
Smith recently linked up with Collingwood star Nick Daicos in the United States and is one of the most marketable figures in the AFL, boasting an Instagram following of more than 340,000.
He has a strong connection to younger fans, having previously spoken about his mental health battles in the spotlight.
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