Henry picked up the injury in the first half of Saturday's 1-0 defeat to Newcastle United following a collision with Kieran Trippier.
The left-back was left clutching his knee, before he limped off the pitch with the assistance of Brentford's medical staff.
The Bees have now confirmed that Henry has sustained an anterior cruciate ligament injury and is now set for an extended spell on the sidelines.
Brentford's head of medical Neil Greg said: "Rico will require surgery in the next week or so and, unfortunately, a prolonged period of recovery.
"Whilst this is disappointing, Rico has been through a similar experience in the past and is already focussed on using this as an opportunity to become fitter and stronger than before. We will support him fully throughout this process."
Henry, who is the longest-serving player in the Brentford squad, previously suffered the same injury against Middlesbrough in September 2017.
News of Henry's injury represents a huge blow for Brentford boss Thomas Frank, who has made the 26-year-old an integral part of his squad.
The defender has missed just five Premier League matches since August 2021, highlighting his importance to the Brentford side.
With Brentford light on options in the full-back area, Frank will have to reshuffle his backline in Henry's absence.
Aaron Hickey is able to play on either side of the defence and is likely to move across to left-back from the right side of the back four.
Should Hickey switch to the left, the right-back position could be filled by Mads Roerslev, who came off the bench to replace Henry against Newcastle.
After suffering their first defeat of the season at the weekend, Brentford will look to bounce back when they play host to Everton on Saturday.