First Lady Michelle Obama refused, but Bronagh Key is set to wear a headscarf when she visits Saudi leadership in Riyadh with her husband John Key.
Mrs Obama caused a minor flurry when she did not cover her head on an official visit to the Kingdom with her husband, US President Barack Obama, earlier this year.
Speaking ahead of the visit, Mr Key said his wife would wear the headscarf as a mark of respect for their culture.
Headscarves are required for women under Saudi law, but exceptions are made for foreigners, with many seeing Mrs Obama's decision as a protest against the treatment of females in the strictly Islamic nation.
The Twitter hashtag #Michelle_Obama_Immodest reportedly trended briefly in Saudi Arabia, while others pointed out that she wore a head scarf on an earlier visit to Indonesia, another Muslim country.
She gained plenty of support from others, who said she had taken a feminist stance.
The likes of Princes Diana and Condoleezza Rice also decided against covering their heads when visiting Saudi Arabia.