The world champions said the German, driving the F2003-GA for the first time, clocked a lap of 57.045 seconds at Ferrari's Fiorano test track to beat the previous record of 57.476.
The previous best was set in the dominant F2002 last July only days before he won his record-equalling fifth championship and with the car in full flow.
The Fiorano track may even be slower now after being resurfaced since then.
Watched by Ferrari president Luca di Montezemolo and sporting director Jean Todt on a cold morning, Schumacher completed 20 laps before lunch with a best time of 58.291 seconds.
That compared to the 58.620 seconds he set in the F2002 on its first run last February.
He then returned in the afternoon to break the record and complete a total of 78 laps.
"Gianni Agnelli would have been proud of us, of the team, of what we have done today; 78 laps straight off without the slightest problem," said Schumacher, who will continue testing on Wednesday.
"Today we achieved a very good result with great reliability. I am very happy with this first day of testing."
The car is named after the late FIAT patriarch Agnelli, head of Ferrari's parent company, who died recently.
The F2002, introduced at last year's Brazilian Grand Prix after a Williams one-two in Malaysia, was beaten only once during the course of the season as dominant Ferrari roared to 15 wins in 17 races.
Schumacher was on the podium in every race and won 11.
The new car is not due to be used in race conditions until the season returns to Europe for the San Marino Grand Prix in April after the three opening 'flyaway' rounds of the championship.
While Schumacher was making his mark, Colombian Juan Pablo Montoya gave Williams's reply with an unofficial lap record of his own as he tested the new FW25's 2003 specification aerodynamic package at the Valencia circuit in Spain.
Montoya set a time of 1:10.15, beating the previous best of 1:10.62 set by McLaren's Kimi Raikkonen.
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