The Red Cross said they needed to temporarily suspend aid activity to understand what had happened.
One official warned that attacks on aid workers in conflict zones could become the norm.
Police believe the ambush in the northern province of Jowzjan was carried out by militants from so-called Islamic State.
A team of three drivers and five field officers had been on its way to deliver livestock materials when their convoy was deliberately attacked, the International Committee of the Red Cross (ICRC) said in a statement.
"Nothing can justify the murder of our colleagues and dear friends," they said.
The aid agency has had an uninterrupted presence in Afghanistan for 30 years.
Mike Adamson, chief executive of the British Red Cross, said there was a "profoundly worrying escalation in loss of life of humanitarian workers".
"They [the latest developments] risk marking the moment that the death of people who should be protected under the international rules of war became the norm," he said.
"We cannot accept that... After each attack comes a chorus of condemnation. Such condemnation is starting to fall on deaf ears."
ICRC director of operations Dominik Stillhart said the agency would "definitely do everything" to resume operations.
The bodies of the six workers were taken to the provincial capital Sheberghan and from there to Mazar-e-Sharif, officials say.
A search is under way for the two ICRC employees who were not accounted for.
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