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.

Mid East Falcons win inaugural United Series Championship in Dubai
UAE to face Morocco in FIFA Arab Cup semi-final
Man City beat Palace, Villa edge West Ham in five-goal thriller
Rodrygo's winner lifts Real Madrid past Alaves to end losing streak
Mid East Falcons win the inaugural United Series Championship in Dubai
