Emergency services rushed to the state's southernmost coastal town, Port Macdonnell, about 11am on Monday after they were alerted to a vehicle with its engine running in a car park near cliffs at Cape Northumberland, police said.
Officers spotted the bodies of an adult and small child in the ocean a short time later.
They have been identified as a 36-year-old woman from Compton, near Mount Gambier, and her toddler.
Police and other emergency services, along with volunteers including local fishing crews, searched for the infant until bad light forced them to stop.
The search will resume on Tuesday morning.
"We do hold grave concerns. The child is less than one-year-old. In any conditions that would cause great concern about the child's ability to survive if not in the water," Superintendent Trent Cox told reporters.
"We're keeping an open mind about everything, but I don't hold out great hope."
Predicted bad weather could hamper search efforts on the water on Tuesday, but Supt Cox said they could still conduct searches of the coastline on foot and using thermal imaging drones.
Police are urging anyone who may have seen the woman's vehicle - a white Isuzu MUX, registration S592BJR - to contact Crime Stoppers.
"The reason we've made that public appeal is that we're trying to build a picture of the woman's movements leading up to her arriving at Cape Northumberland," Supt Cox said.
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