Thirty-four other people making the same journey from Mexico were rescued by border patrol agents aided by the Nogales police and fire departments, the Arizona Daily Star reports.
"Our agents were pulling people out of the water and saw four people swept away," Sean King, a Border Patrol spokesman said.
Police and firefighters were unable to locate the four after searching for hours from the point of the rescue to the city limits.
"There was no trace of anybody but we will continue to be watchful," city spokesman Juan Pablo Guzman told the newspaper.
The tunnel where the 34 were found is a flood-control system for cities on both sides of the border.
Authorities said it had been swollen to flash-flood levels by overnight rains.