The American pulled out of the event on Wednesday with a back problem, while Azarenka withdrew on Monday due to a bruised heel.
Williams has had $50,000 forfeited from the WTA’s bonus pool, while Azarenka has copped $100,000.
The Belarussian’s heftier fine is a result of pulling out late 12 months ago in similar circumstances.
The duo have also had zero points imposed on them for one tourmanent, however both punishments are unlikely to have any major effect to either.
Earlier this week, Williams became the number one women’s player in the world, ahead of Azarenka.