Warburg was understood to be seeking to place the stock at about 625p a share. Johnson Matthey closed down 20p at 630p.
The company - which is owned by Anglo American, the Oppenheimer family and De Beers, and chaired by Julian Ogilvie Thompson - explained that the sale of the 9.9 per cent holding was part of a programme of disposals designed to strengthen the company's balance sheet as it prepared to develop several significant mining projects around the world.
Explaining that the stake had been a "non-strategic investment", a Minorco spokeswoman said that the company had been "a totally different animal" when the Johnson Matthey shares were acquired from Charter Consolidated at 490p in February 1993.
For example, Minorco had wanted to be exposed to the platinum market, she said.
Recently, Minorco acquired several mines at various stages of development and estimates that these will require funding of about $2bn, half of which will come from the Minorco balance sheet. As a result, Minorco is looking to increase its cash assets.
In February this year, Minorco sold a 9.6 per cent holding worth about $82m in US oil and gas company Santa Fe Energy Resources.
A month later, it received a total of about $250m by disposing of an 18.9 per cent stake in Australian mining group Normandy Mining and a 3.7 per cent interest in the company's gold mining arm, PosGold.
The spokeswoman said Minorco would be reviewing the situation and selling other investments as the need arose.
Last year, Minorco, whose chief executive is Hank Slack, announced a 51 per cent increase in underlying profits, to $365m.