The 59-year-old guard did not appear to be seriously injured, but she had a bruise on her face after the attack, said John Sayers, principal of nearby Russell Elementary School.
"She was more upset about the children having to see that than what happened to her," Sayers said.
The crossing guard, whose name was not released, was helping about 20 children across a street in the unincorporated Florence area of South Los Angeles when she tried to stop an SUV on Monday, the sheriff's department said.
As the vehicle drove toward her, she held her sign aloft and said, "'You have to stop, the children come first,"' according to a police statement.
Authorities said the driver, Jose Hernandez, 27, yelled that he was not stopping. As he was shouting, his girlfriend, Vanessa Del Pilar Martinez, 20, left the SUV.
When the guard tried to walk away, Martinez punched her and knocked her to the ground, authorities said.
Detective Frank Heredia said the driver then got out the SUV and grabbed the guard's stop sign as Martinez yanked her whistle and ID tag from around her neck. Some witnesses told investigators they saw the driver punch the guard, too.
Heredia said the motive was unclear, but the incident was likely triggered by road rage.
"They had a place to go and they were in a hurry, then the crossing guard was there," Heredia said.
Heredia said the couple may have decided to take guard's crossing equipment as a souvenir.
Several adults took down the license plate number of the SUV, and deputies later arrested the two suspects for investigation of robbery. They were being held in lieu of $50,000 bond with arraignment set for Wednesday.
They had not yet been assigned attorneys.
Children who witnessed the attack were offered counseling, Sayers said.
Margo Minecki, a spokeswoman with the county's department of education, said it was the first time she had heard of a crossing guard being attacked.
"The guards may face some hostility from motorists, but none has been beaten up," Minecki said. "It really doesn't happen."