The elephant attacked the woman - and the man died after trying to rescue her from being trampled by the animal.
Police in Zambia said the holidaymakers were killed on Saturday while on safari.
"A lady from Belgium aged 57 and a 64-year-old man from the Netherlands were killed as they went close to the elephant trying to take photographs," said police spokesman Danny Mwale.
The pair were visitors at the Maramba River Lodge in the town of Livingstone and were watching the animals as they came close to the lodge.
According to ZNBC news, one elephant charged at the Belgian woman after she approached it. The Dutch man was trampled as he tried to rescue her.
African media reports described "an influx" of elephants in Livingstone and cited another elephant attack in which a security officer was trampled on his way to work.