The 24-year-old left-sided player, who has been with the club since 2016, has signed a contract taking him until 2026.
Henry has played 150 games for the Bees, and is a key reason for their impressive form in the Premier League this term.
Brentford boss Thomas Frank said in a statement: "I am very pleased that Rico has signed another contract with us. He has had a top time here. He has been here a long time, and we are pleased that he wants to continue to grow with us.
"Rico has seamlessly made the step up to the Premier League. Defensively he is fantastic, and you can see the way he defends one on one against some great attackers. He is also contributing up the field with the way he can arrive in the penalty area, as we have seen this season. There are bits to work on, but it is great that he will continue that development with us.
"We are pleased that we have a player here that can develop in to a good Premier League player. He can also be part of our development as a club. We are constantly aiming to be better. We think we can get to a higher level and think we can take Rico to a higher level as well. It is very good to have him here."