Sharapova, hoping to complete her set of Grand Slams with victory at the French Open, had added the Stuttgart clay court event to her calendar to prepare for next month's tournament at Roland Garros.
Cornet, however, gave her a short start on the indoor clay courts retiring with a shoulder injury while trailing 6-3 1-0.
"It was (qualifier) Alize's fifth match in five days. Tennis is very tough on the body," said Sharapova, who wants to get clay court practice ahead of Paris.
"Practising helps but matches are always a bit different. You have to get used to the different match situations and opponents with different styles," she told reporters.
Former world number one Caroline Wozniacki advanced to the second round by the same score after fellow Serbian Jelena Jankovic also retired injured.
Germany's Mona Barthel sent Ana Ivanovic packing 7-5 7-6 to confirm her fine form this year and set up a second round clash with seventh seed Marion Bartoli.
"This was something special because Ana used to be a bit of a role model for me," Barthel told reporters. "I was still in school when she won the French Open and I watched it on TV. That was at the time a long way for me."
Wild card entrant Barthel, who won her maiden WTA tournament in Hobart earlier this year, saved two set points against the former world number one in the first set and fired a total of 11 aces as she breezed past Serbian Ivanovic.
Hungary's Greta Arn initially troubled Agnieszka Radwanska with her powerful backhand with each player grabbing an early break before the Polish world number four broke her again with a fine crosscourt smash to move 4-2 up and hold serve to clinch the first set 6-3.
Arn rescued a break point to hold serve with yet another sublime backhand and lead 3-2 but Radwanska got the necessary break a little later to win 6-3 6-4 and became the first quarter-finalist when the Hungarian sank a forehand return into the net.
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