The site, on Newington Causeway near Elephant and Castle, will contain 38 flats and three floors of shops.
Southwark Council's planners approved the scheme by four votes to three.
The club said it was "extremely disappointed" and thought the decision was "wrong".
It had fought the proposals, fearing people moving into the flats could submit complaints about noise levels which might lead to the venue closing.
The council said the new block was in "a prime location" in central London and part of the regeneration area around Elephant and Castle.
"Any improvement to this area would be of great benefit to local people," said Councillor Fiona Colley, the borough's cabinet member for regeneration.
"We appreciate that the Ministry of Sound is a valued club, business and local employer which we have no intention of seeing close.
"I believe the club can and will remain open alongside new residential developments," she added.
But Lohan Presencer, the venue's chief executive, said his firm was taking legal advice "and will be doing everything we can to prevent this catastrophic threat to the future of our business".
"We believe that the council has mishandled this application, failed to understand or acknowledge its implications at every turn and that they have now misdirected their councillors to the wrong decision," he said.
The club collected 25,000 signatures when opposing the previous development, which proposed 315 homes on the same street.
The musician Example was among those speaking out about the proposal, which the council rejected on the grounds of noise and as it did not meet requirements for affordable housing.

GB started nervously and struggled with their offence in the opening half, falling 29-20 behind at the interval.
But they drew level midway through the third quarter to give themselves hope.
However, the USA pulled away again towards the end of the quarter and their defence also restricted GB's shooting opportunities.
Steve Serio did much of the damage with 20 points for the USA, who avenged their defeat to GB at the same stage four years ago.
Great Britain, beaten in the semi-final 69-52 by Canada, were unable to make the most of their early opportunities and Serio, celebrating his 25th birthday, capitalised to help build up a 17-10 lead after the first quarter.
The introduction of forward Joe Chambers, who hit eight points in a row at the start of the second quarter, enabled the USA to stay in control.
The game is evolving and getting quicker and it is very hard to get quicker when you get to your mid-30s
GB started the second half with far more purpose and Terry Bywater and Ian Sagar inspired the comeback to level the game at 29-29 with four minutes and 55 seconds to go in the third quarter.
But once USA coach Jim Glatch brought Joshua Turek, Matt Scott and Serio back into the game, they settled back down and dominated, forcing GB into difficult shooting positions, and it gave them a first medal in the sport since Sydney in 2000.
Afterwards, coach Murray Treseder was realistic about his British team's performance.
"We've finished fourth and that's probably where we are at the moment," he said.
"We started nervously and they got on top early on, but we made too many mistakes. I admired our fight in the third quarter but when we got back to 33-all, we made five errors and that just killed us.
"We were chasing our tail in the last quarter as we tried to get back in the game, but give the USA credit, they are a great team."
The Australian has also hinted at changes as the team look to Rio in 2016, starting with next year's European Championship in Frankfurt.
"We have an outstanding junior development programme with lots of hopeful players," he added. "The game is evolving and getting quicker and it is very hard to get quicker when you get to your mid-30s.GB miss out on basketball bronze
"I think the standard we have seen here is quite considerable and we have got to respond to that. I think finding some new low-point players is critical for us and we will go from there."
Patrick Anderson confirmed his status as the player of the tournament as he led Canada to gold.
The 33-year-old, who came out of retirement last year, contributed 34 points, 10 rebounds and eight assists in their 64-58 win over Australia.
Although Australia led early on, Anderson sparked the run that put Canada on top at the start the second quarter, and then helped them pull clear in the third.
"It feels like I have never won anything in my life," Anderson said on collecting his third Paralympic gold. "I feel like a little kid."
A 22-storey tower block has been approved close to the site of the Ministry of Sound nightclub in south-east London, three weeks after another development nearby was rejected.
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Great Britain missed out on a third consecutive men's wheelchair basketball Paralympic bronze medal after losing 61-46 to the United States.