She had previously beaten McHale at the 2014 Italian Open second round.
She is expected to hear from Roland Garros on Tuesday about the status of her wild card request.
Two-time champion Maria Sharapova has not been given a wild-card entry for the French Open.
Sharapova tested positive for meldonium at the 2016 Australian Open and her original two-year ban was reduced on appeal.
While Stosur stumbled on her preferred surface there were no issues for Maria Sharapova.
The federation chief had hinted Sharapova would not be welcome after agreeing with comments made by Andy Murray in March, in which the Briton said she should have to work her way back to the top.
He felt that offering Sharapova a short cut into the main draw was to send the wrong message in the fight against doping in sports.
"I am very sorry for Maria, and very sorry for her fans".
"I know that a lot of people might be disappointed by this decision".
Warriors' Kerr returns to practice for 1st time in 3 weeks
As Golden State went into halftime trailing by 20 points, Kerr did his part to talk the team through their slump. We'll be all right". "It's great any time you can hear his voice, see his face", Warriors guard Steph Curry said.
It completed a miserable evening for the five-times grand slam champion, now ranked 211, who earlier found out that she had been refused a wildcard for the French Open. It was inconceivable to take a decision that would have been the opposite of this. I certainly have expectations of myself.
But once the second set began, Sharapova was in control and began to resemble the player who won the trophy at the Foro Italico in 2011, 2012 and 2015.
She is now back in professional action although her lack of ranking points means she is relying on wildcards to get into tennis' biggest tournaments.
Although Sharapova said she was unaware of her status for Wimbledon, the tournament's officials have apparently been highly aware of her potential presence at its qualifying event. Today that suspension is over and she can take her path towards the new success.
"Winning matches will get me places, so if..."
On the other hand, Lucic-Baroni caused Sharapova some problems in Madrid last week but she was unable to sustain her level of play.
Sharapova got another wild card for the Madrid Open last week. Nonetheless, the competitive edge from the three-time Internazionali BNL d'Italia champion has not wilted.
In Stuttgart, WTA CEO Steve Simon told German broadcaster ZDF she had paid the price.