Wissa, 28 opened the scoring inside 30 seconds against champions Manchester City on Saturday, but was then substituted just before half-time following a challenge with Mateo Kovacic in a match the Bees eventually lost 2-1.
Frank, speaking ahead of Tuesday's League Cup tie against fellow London side Leyton Orient, told reporters: "Wissa is not good news. It looks like an injury that will be a couple of months. It is very frustrating.
"It will leave a hole, but I will find a solution and other players will step up."
Brentford are already without pre-season signing Igor Thiago because of a knee injury, while England striker Ivan Toney has left for Saudi Pro League club Al-Ahli.