Schumacher is still attempting to turn around a poor season. He hasn't won in Monaco since 2001, his longest winless streak at any race on the circuit.
Earlier in the day, Raikkonen gained his third consecutive pole position. It may be the last time qualifying is spread over two days after the teams voted unanimously to change to Saturday qualifying only with a vote this week.
BAR-Honda was missing from the race as it served the second part of a two-ran ban.
The late Prince Rainier III was remembered before the race with a minute of silence. Prince Rainier died April 6 at the age of 81. He was a fixture at the race and missed only the 2003 race with illness.
Bruno Junqueira won a crash-marred Monterrey Grand Prix, during which previous winners Sebastien Bourdais and Paul Tracy knocked out each other from the race lead on Sunday.
Junqueira grabbed the lead for good on the 67th lap, overtaking England's Bjorn Wirdheim. A yellow flag slowed the action two laps later, allowing the Brazilian to cruise to victory.
Only 10 of the 19 cars in the field completed the 76-lap Champ Car World Series race.
Canadian Andrew Ranger finished second, 1.376 seconds off the lead. Countryman Alex Tagliani was third, 2.847 seconds behind Junqueira.
Another Canadian, Tracy, and defending champion Bourdais battled for the lead during the first half of the race before the two crashed on lap 48.
Running second, Bourdais tried to pass Tracy, but collided and rolled over his front tire. Tracy was knocked out of the race, while Bourdais was forced to pit and fell back to 12th.
Bourdais finished fifth, more than 9 seconds off the lead. England's Justin Wilson was fourth.
It was Junqueira's first victory since winning in Australia last October. He finished third at the season-opening race at Long Beach, California in April, and placed second behind Bourdais in last year's Champ Car standings.
The afternoon's first yellow flag came on just the ninth lap, when rookie Timo Glock of Germany fishtailed around the fifth turn and stalled. Four laps later another rookie, Ronnie Bremer, spun out and stalled on the grass to the right of turn six.
Brazil's Ricardo Sperafico lost a tire on the 32nd lap, hitting the wall. Things then stayed relatively clean for a while, but the yellow flags came out in earnest again late.
After Bourdais forced Tracy out of the race, Jimmy Vasser hit Mexico City native Mario Dominguez eight laps later, ending the day for both cars and triggering another caution.
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