Wissa sustained the injury in the first half of Saturday's 2-1 defeat against Premier League Champions Manchester City.
The 28-year-old enjoyed a successful start to the contest, finding the net after just 22 seconds to give the Bees a surprise lead.
However, the half ultimately ended in disappointment as Erling Haaland netted a quickfire brace, before Wissa was forced off following a heavy challenge from Man City midfielder Mateo Kovacic.
Speaking about the incident after the match, Frank told reporters: "It was a reckless tackle, I thought, from Kovacic, just going through the man, from behind him. I know it's probably not a red card, but it's frustrating that it's led to an injury."
Frank confirms extent of Wissa injury
The Brentford head coach has now confirmed that Wissa has sustained an ankle injury which is set to keep him out until November.
"Wissa is, unfortunately, not good news - it looks like an injury that will be a couple of months," Frank told reporters ahead of Tuesday's EFL Cup clash with Leyton Orient.
"It's very frustrating. We talked about our many injuries last year, I hope I don't have to talk too much about it this year, I maybe already have.
"We were unlucky with [Igor] Thiago, unlucky with [Aaron] Hickey. We've then had two contact injuries with Mathias Jensen and Yoane Wissa, so that's very frustrating.
Brentford light on forward options
The DR Congo international had enjoyed a positive start to the new season, scoring three goals and providing an assist in Brentford's first four league games.
Wissa's performances have softened the blow of Igor Thiago's knee injury and Ivan Toney's departure to Saudi Pro League side Al-Hilai.
With Wissa set for a spell on the sidelines, Frank will have to turn to other members of his squad to support Bryan Mbeumo in attack.
Brentford will look to negotiate Tuesday's third-round EFL Cup tie against Leyton Orient, before they face Tottenham Hotspur in Saturday's Premier League away clash.
Having collected six points from four league games, the Bees are currently sitting in ninth position in the standings.