Kevin Schade's early strike proved enough to edge out the Hammers last weekend, securing Brentford a third consecutive away victory.
However, they were unable to make it through the away clash unscathed after Van den Verg was forced off on the hour mark at the London Stadium.
Frank has now allayed fears that the centre-back sustained a serious injury, although he will be out for the foreseeable future due to a minor problem.
Frank provides Van den Berg update
"Sepp got a minor knee injury," the Brentford boss told reporters ahead of Friday's clash against Leicester City at the King Power Stadium.
"It's good news. You're always a little bit worried with the knee, but it's a minor one and we're talking about weeks instead of months.
"How many weeks, it depends on how quick he is recovering. Straight after the game I was hoping it was a minor one, so I'd say it's as positive as it can be."
While it will be a relief that Van den Berg has avoided serious injury, his absence will still come as a blow given the fact that he has been a regular fixture in the Brentford side since arriving from Liverpool last summer.
The former Netherlands Under-21 international has started 20 of his 21 Premier League appearances this season.
Who will replace Van den Berg?
Ethan Pinnock played the final half-an-hour in last Saturday's clash with West Ham after he came off the bench to replace the injured Van den Berg.
As a result, Pinnock is the obvious candidate to form a centre-back partnership with Nathan Collins for Friday's meeting with relegation-threatened Leicester.
Alternatively, Frank could hand a starting place to the experienced Ben Mee, but that seems unlikely as he has not started Premier League games since the end of December.
Meanwhile, the Bees are still having to cope without Aaron Hickey, Rico Henry, Josh Dasilva, Gustavo Nunes and Igor Thiago.
Written by
Ben Sully