"This remarkable car has achieved a world record price for a modern-era Formula One," the Sotheby's auctioneer said after the F2003-GA, Chassis 229 car went under the hammer for 13 million Swiss francs ($13.2m).
When taxes and fees were added, the final price was 14.6 million francs, the auction house said later.
The previous record was held by another Schumacher-driven Ferrari, an F2001 model sold by Sotheby's in New York in 2017 for $7.5m.
The final price, offered by an unidentified telephone bidder from Europe after a bidding war of more than 40 minutes, far outstripped expectations.
The auction house estimated before the sale that the car would fetch up to 9.5 million Swiss francs.
It is "one of the most significant Formula One cars of all time", the auctioneers said.
Schumacher, who has not been seen in public since suffering serious injuries in a skiing accident in 2013, raced nine times in the car.
He won five Grands Prix with it in the 2003 season and drove it when he clinched the title in Japan.
"It's one of the Ferraris with the most victories in the constructor's history, so it's a very important car in the history of motor racing," Vincent Luzuy, from the Sotheby's branch dealing with luxury car sales, told AFP.
Designed by Rory Byrne and Ross Brawn, the F2003-GA had a longer wheelbase to improve aerodynamics, Mr Luzuy said.
The model was brought in at the Spanish Grand Prix, the fifth race of the 2003 season. Chassis 229 is by far the most successful of the six F2003-GAs that were built.
Schumacher drove it to victory in Spain and also won the Austrian, Canadian, Italian and US Grands Prix in it.
The car powered Schumacher to his sixth F1 title, breaking the record of five won by Argentina's Juan Manuel Fangio in the 1950s.
It also helped Ferrari to win a 13th constructor's championship — the Italian team's fifth in a row.
Schumacher's Ferrari was sold during Sotheby's Luxury Week, which began last Friday, where sparkling jewels, pricy watches and designer handbags are going under the hammer.
But a spectacular blue diamond, expected to provide the grand finale to the jewellery sale and estimated to fetch up to 15 million Swiss francs, went unsold later on Wednesday.
That 5.53-carat "fancy vivid blue" cushion-shaped diamond is part of the De Beers Exceptional Blue Collection — eight rare fancy blue diamonds with a total value of more than $70 million, being sold in Geneva, New York and Hong Kong.
Sotheby's told AFP the gem was "an exceptional stone in every sense" and "attracted significant interest" before the sale.
"While we didn't get to see it sell in the room tonight, we are confident it will find a new home very soon," the company said.
Another piece expected to draw attention, and bids, was an emerald and diamond bracelet made in the 1850s, which once belonged to French empress Eugenie, the wife of emperor Napoleon III.
It has been estimated at between 60,000 and 80,000 francs.
Sotheby's is already on a roll, having sold the 11.15-carat Williamson Pink Star pink diamond in Hong Kong last Friday for HK$453.2m ($57.7m), setting a record for price per carat paid at auction for any diamond or gemstone, it said.
Pink diamonds are only found in a few places and fewer than 10 per cent weigh more than one fifth of a carats. The big ones are some of the most in-demand on the global market.
The 18.18-carat Fortune Pink — the largest pear-shaped "fancy vivid pink" diamond ever to go under the hammer — was snapped up at a Christie's auction in Geneva on Tuesday for $28.5m.