"We've exhausted all our resources at this point," Oakland Fire Department spokesman Lt. David Brue said today.
Brue said authorities think fast-moving water may have swept the baby, John Uaisele, a mile or more from the site of the accident.
He said a fire department search and rescue team "worked methodically" to try to find the boy Monday but didn't have any success.
The boy was riding in a pickup truck with his family during a rainstorm around 7:30 p.m. Saturday when the truck crashed near Hamilton Street and Hegenberger Expressway, landing on its roof in a nearby flood control channel.
The boy's father and the driver of the vehicle, Petelo Uaisele, was killed.
Four other people in the car, including the boy's mother and 1-year-old sister, were injured.
Oakland police said the accident appears to have occurred when a limousine bumped the rear of the pickup truck, causing Petelo Uaisele to lose control.
Brue said the search crews had waded through several waterways on both the eastern and western sides of Interstate Highway 880 near the Oakland Coliseum, including the Damon Slough.
He said the crew then used boats to search the deeper waters of San Leandro Bay near the Martin Luther King Jr. Regional Shoreline.
Brue said other crewmembers searched an area next to the Robert Crown Memorial State Beach in Alameda, several miles away.
The Uaisele family, as well as fellow members of the Tongan community and the family's church, the Mormon Temple in Oakland, also jumped in the Damon Slough and other locations to look for the infant.
Although the search could resume at a later time, it does not appear likely that will happen today, Brue said.