Hundreds of officers in riot gear responded to a Thursday demonstration, using batons and non-lethal projectiles to disperse the protesters, the Los Angeles Times reported.
Some protesters threw bottles and cans at officers and chanted, "Whose streets? Our streets!"
The report did not provide details on the two officers' injuries.
Witnesses said the clash apparently was preceded by a chalk-drawing demonstration.
A woman who identified herself as part of Occupy LA said protesters intended to show support for people previously arrested for using chalk on sidewalks.
"We were handing out free chalk for freedom of speech," said Cheryl Aichele, 34.
Messages written at Spring and 5th streets included, "May the youth rise" and End the Fed."
Witnesses said an unidentified man who threw a glass bottle that landed in front of police officers on Spring Street was shot with what appeared to be a non-lethal weapon.