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.

Brook's defiant ton in vain as New Zealand beat England
Bencic tames Noskova to win Tokyo title
We need to find answers to stop Liverpool slide, says Slot
Rohit and Kohli bid likely farewell to Australia as winners
