Hickey missed Saturday’s thrilling 3-2 victory over West Ham after picking up the problem in training on Thursday, adding to the list of injury headaches that have disrupted Frank's plans all season.
The Bees are already missing first-choice left-back Rico Henry, who suffered a serious ACL injury earlier this season, and Hickey, a right-back by trade, has been deputising on the opposite flank.
However, the Scotland international is now set to miss at least two months of the campaign, including the busy festive period, with what Frank called a “high-grade” injury.
Despite Hickey’s absence, the Bees made it three consecutive Premier League wins with their triumph over the Hammers, centre-back Nathan Collins heading a second-half winner to settle a rollercoaster affair.
The home side had opened the scoring early on through Neal Maupay, who return to Brentford on loan from Everton this summer and finally put an and to a 34-game goal drought stretching back well over a year.
"I’m smiling,” Frank said. “I’m so pleased for him. I know him very well and in the last three weeks he’s showing more and more in training of the Neal I knew. Sharp touches, goals, good finishes, on it, driving things in training. More and more confident getting up to his best level.
“He’s looking good in training which is very important. Now he’s got the goal and will get a bit more confidence on the pitch every Saturday.”