The 26-year-old, who toured with the Lions in 2005 playing in the second Test in Wellington, saw a specialist on Tuesday and will be out of action for a month.
"Unfortunately he's going to be ruled out of the rest of the autumn series," said Wales and Lions coach Warren Gatland.
"He's a world-class player and when he's fit he does make a difference. We're just hoping he gets fit and back and available to us, because on his day…he is able to compete with the best players in the world.
Wales face Canada, New Zealand and Australia in their remaining November Tests but Henson will now have to wait until next year's Six Nations to prove his Lions credentials on the international stage.
"Consultations with UK specialists led us to conclude that an injection, followed by a specific rehabilitation protocol which will take place over the next few weeks, was the best way forward," said Wales team physiotherapist Mark Davies.
"Gavin has now had his injection and will be out of action for approximately one month.
"He has been given an injury-specific training programme to follow in that time, which should provide a resolution to his problem."
The news is the latest setback in Henson's recent career, with injury and suspension meaning he has played just three full games since his 2007/08 season ended prematurely in April.