Kanepi was due to face Wozniacki in the first round of the WTA Premier event, but the Dane was forced to bow out through injury.
"Sad I had to withdraw from Stuttgart today," she tweeted. "Sorry to everyone who was gonna come out to support me!"
Johanna Konta was drafted in to take Wozniacki's place as a 'lucky loser', with the Brit having gone down in qualifying to Italy's Gioia Barbieri earlier in the day.
Yet Konta was unable to cause an upset as Kanepi claimed a 7-6 (7-4) 6-4 victory in just over an hour and a half.
Kanepi fell a break behind in the first set, but broke back immediately before reeling off five consecutive points to win a tie-break.
The second set followed a similar pattern, with Konta initially moving 2-0 ahead before giving up her advantage.
Kanepi will face Sara Errani or Klara Koukalova in round two