The influential defender has missed more than a month with nerve damage that has affected his right leg.
Fulham had hoped to bring the 32-year-old back to full fitness without the need for an operation.
But now the Norway defender has had to bite the surgery bullet, and will need six more weeks to recover.
New Fulham boss Meulensteen conceded his absence will be a big loss during the pivotal Christmas period.
He said: "Brede is a bit of a disappointment to be honest, because we have looked at all medical strategies and it's a bit of an awkward one.
"He's seen another surgeon and a specialist and I think they have decided that they're going for the surgery, which will keep him out for at least six weeks.
"But on a positive note we know now, there's clarity.
"And the one thing that I want for such an important player for us, is that he can focus on the rehabilitation so when he comes back he will be like a new player for us."
Fulham host Aston Villa at Craven Cottage in Sunday's lunchtime kick-off in the Barclays Premier League, seeking to hit back from Wednesday's 2-1 Tottenham loss.
Striker Darren Bent is unable to face his parent club due to the terms of his loan deal, while Kieran Richardson is a doubt after illness and hamstring trouble.
Defender Phillipe Senderos is fighting a thigh problem, while Hugo Rodallega will not make a return to training until next week.
Meulensteen admitted he hopes former Arsenal centre back Senderos will beat his thigh complaint in time to face Paul Lambert's Villa side.
"Phillipe gave a monstrous performance (against Tottenham), he had a bit of a thigh strain," he told Fulham's official website.
"But the way he played himself through it was characteristic of the performance, and I paid him a big, big compliment about that.
"Darren (Bent) is not allowed to play because of the loan deal.
"Kieran we have to assess, unfortunately he couldn't be in on Friday because of illness, so we need to monitor that as well.
"Further than that I think obviously Hugo Rodallega is still working back to fitness and will come back to training with us next week."