Henry suffered the injury during practice, and an MRI confirmed it shortly thereafter.
"Results revealed a completely torn Achilles," a source told ESPN.com.
Henry is scheduled to have surgery Tuesday morning with Dr. Neal ElAttrache and Dr. Steve Lombardo of the Kerlan-Jobe Orthopaedic Clinic in Los Angeles.
Though the team is just 14 games into its 2014-15 campaign, Henry is already the third Laker to be declared out for the season because of an injury, joining point guard Steve Nash (back) and rookie forward Julius Randle (leg). Reserve forward Ryan Kelly is currently sidelined because of a hamstring tear.
Injuries plagued the Lakers dating back to last season, when their players missed a league-high 319 combined games because of injuries.
Lakers coach Byron Scott said Henry suffered the injury during a three-on-three drill.
"Nobody hit him or anything like that," Scott said after practice. "He went down and pretty much said to us that he heard a 'pop.'"
The oft-injured Henry has had knee injures the past two seasons and even went to Germany this offseason for treatment. In nine games with the Lakers this season, Henry averaged 2.2 points over 9.6 minutes.
With four players sidelined in Nash, Randle, Kelly and Henry, it's expected that the Lakers will apply for a hardship exception from the NBA to add a 16th player to the roster, one more than the regular-season maximum. Once Kelly returns, the Lakers would need to trim their roster back down to 15.
The Lakers would also be eligible to apply for a disabled player exception that allows the Lakers to spend on an additional player. The exception would be worth half of Henry's salary, about $550,000. They were already granted a $1.5-million disabled player exception for Randle.
Disabled player exceptions cannot be combined, meaning the Lakers wouldn't be able to package the exception for Randle with a potential exception for Henry to acquire a player for $2 million.