However, one of the New Zealand aid workers was asked to stay in Kandahar with a few key personnel until further notice.
The organisation said full security measures have been put in place.
"This incident again highlights the growing violence against health-care workers, facilities and beneficiaries remaining one of the most serious humanitarian challenges in the world today. And yet it frequently goes unrecognised," the New Zealand Red Cross said.
"A single act of violence that damages a hospital or kills health-care workers has a knock-on effect, depriving many patients of treatment they would otherwise have received from the facility or workers in question."
A third New Zealand aid worker is also based in Kandahar but was on leave at the time of the attack.
New Zealand Red Cross supports humanitarian aid workers and has international programmes in more than 15 countries.