The world number one lost on Tuesday night in straight sets to Dubai resident Kristina Mladenovic.
Meanwhile, fourth seed Karolína Plíšková is through to the next round after beating Dominika Cibulková in three sets.
Petra Kvitová, the 2013 Dubai Duty Free Tennis Championships winner, is in action later Wednesday.
The second seed takes on the USA's Jennifer Brady on Centre Court at 11:00 am.
Simona Halep, Angelique Kerber and two-time defending champion Elina Svitolina also play their round of 16 matches later today.