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.
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.