The two sides failed to even get onto the wicket after the bad weather that forced a premature end to England’s DLS-assisted defeat to Ireland at the same venue stuck around.
With not even a single ball bowled, the two teams both receive a point, which moves New Zealand top outright in Group 1 and gets Afghanistan off the mark.
The former had thrashed hosts Australia in an 89-run rout on Saturday to start their tournament off, while the latter had been downed by England in a five-wicket loss the same day.
No result hands a lifeline in particular to England, who face Australia, New Zealand and Sri Lanka with just one win under their belt following their shock loss on Wednesday.
The Black Caps will next play Sri Lanka in Sydney, while Afghanistan will remain in Melbourne to face Ireland.