The Scotland international, who joined the Bees in 2022, has been a regular fixture in the Brentford side this season, starting in nine Premier League games.
However, he was absent from the matchday squad for Saturday's Premier League home win over fellow London side West Ham United.
Speaking after the 3-2 victory, Brentford boss Thomas Frank confirmed Hickey will miss the remainder of the year after sustaining an injury in training.
Frank told reporters: "It's a hamstring injury that he picked up on Thursday and it will be a long one. Unfortunately, he will definitely be out for the rest of this year."
News of Hickey's injury will come as a blow to Brentford, who are already having to contend with a number of absentees.
Rico Henry is set to miss the remainder of the season due to an anterior cruciate ligament injury, while Kevin Schade is sidelined after undergoing surgery on an adductor issue.
Mikkel Damsgaard, Keane Lewis-Potter and Josh Dasilva are all still working their way back to full fitness following spells in the treatment room.
In Hickey's absence, Brentford fought back from 2-1 down against the Hammers to record a third consecutive victory.
Neal Maupay scored his first goal since rejoining the club to give Brentford the early advantage, but strikes from Mohamed Kudus and Jarrod Bowen saw West Ham go into the break with a slender advantage.
A Konstantinos Mavropanos own goal pulled the Bees level, before Nathan Collins netted the winning goal to lift the Bees into ninth position.
Brentford, who have collected 16 points from 11 games, will now start preparing for Sunday's difficult away meeting with Liverpool.