The bodies of the boy's 36-year-old mother and 23-month-old sister were recovered in waters off South Australia's southeast coast on Monday.
Superintendent Trent Cox said "extremely challenging" conditions meant emergency vessels had not been able to conduct searches on Tuesday.
"Sadly, today we have not been able to locate the boy, but we will resume the search tomorrow morning," he said.
"Today's search has been confined to land searches, revisiting some of the ground we covered yesterday, but also covering additional ground.
"We will continue to leave no stone unturned … but the search has been suspended as of 3.30pm. It became too dangerous to continue."
The search is focused on Cape Northumberland, the state's southernmost point, at Port MacDonnell on the state's Limestone Coast.
Survivability experts had told police "it is very, very unlikely that the missing baby has survived to this point", Supt Cox said.
Police were alerted to an abandoned car that was left with its engine running near Cape Northumberland about 11.15am on Monday.
The bodies of the woman from Compton, a small community near Mount Gambier, and her daughter were found in the ocean soon afterwards and retrieved with help from local fishermen.
SA Police Commissioner Grant Stevens said he had not had direct feedback on how the fishermen were coping.
"But I'm sure we can all put ourselves in their shoes - it would be heartbreaking and very difficult," he said.
Police had spoken to the woman's husband, who was the father of the children, Mr Stevens said.
The search was being conducted on the belief the missing boy had fallen from the cliff.
"Despite the weather today, which is not good, searching is continuing for the infant," Mr Stevens said.
"Searching for a small child and recovering a woman and a child from the water will take its toll on people who are involved in that search exercise."
Earlier, police said there was "no information to suggest that any other persons are involved in the incident and reports will be prepared for the coroner''.
SA Premier Peter Malinauskas said there were a lot of unanswered questions, making it difficult to understand exactly what transpired.
"These types of tragedies are the ones that shock you to the core," he said on Tuesday.
"If it involves children, that breaks your heart, particularly when we know there is currently a two-month-old baby that is missing, and that's hard to get your head around."
Major Crime detectives and specialist forensic officers are at the scene.
Local mayor Kylie Boston said such tragedies were ''always difficult for smaller communities''.
''Everyone's just a little bit shocked at the moment," Southern Limestone Coast Council's Ms Boston told AAP.
"We'll let the police do the work they need to do, and everyone will just continue to support everyone."
Anyone who saw the woman's car, a white 2015 Isuzu MUX with SA registration S592 BJR, or has any dashcam footage should contact police.
Lifeline 13 11 14
beyondblue 1300 22 4636
