"It was just like mine, same thing," said Bryant. "[He] just tried to take off, drive to the basket and it just popped."
Bryant ruptured the Achilles' tendon in his left leg near the end of the 2012-13 regular season. He returned briefly last season, but suffered a knee injury that limited him to just six games for the year.
Henry suffered a similar injury, to the same leg. He underwent surgery Tuesday at the Kerlan-Jobe Orthopaedic Clinic, operated on by Dr. Neal ElAttrache and Dr. Steven Lombardo.
An Achilles' tear is one of the most difficult injuries to recover from.
"Having just gone through it, I completely understand. He's really frustrated," said Bryant of Henry. "I tried to tell him ... you'll bounce back just fine. You've got to find the positives and you've got to try to find the silver lining."
The 6-foot-6 swingman will miss the remainder of the year, but could recover by the start of the 2015-16 season -- although he's currently on a one-year, $1.1-million contract after re-signing with the Lakers over the summer.
Through nine appearances, Henry averaged 2.2 points a game. Before the injury, he was trying to regain his form after spending most of the off-season working his way back from knee and wrist surgeries.
Bryant is currently the NBA's leading scorer at 26.7 points a game.