A Haumoana resident, who saw the family just before the incident, said they appeared to be playing, and nothing seemed to be wrong.
He said in the space of ten minutes between him leaving to speak with some friends and returning, the two children had gotten into trouble. He did not see the woman.
He watched emergency services bring two children to shore, who he thought were around the ages of 7 and 12.
Police waders are scouring the river mouth of the Tukituki River, which lets out near the beach.
Searchers in the water. Photo/Warren Buckland
A St John Ambulance spokeswoman said they were called just before 5pm to a water incident on Domain Road, Haumoana.
"We sent one ambulance and transported two patients with moderate injuries to Hawke's Bay Hospital."
They could not provide the patients' names or genders.