Police declared a gathering outside the city's convention centre unlawful and made 35 arrests, as stones and water bottles were thrown.
Mr Trump was in the city near the Mexican border to hold a rally ahead of the 7 June California primary.
He has pledged to build a border wall to keep out illegal immigrants.
The skirmishes flared as the convention centre emptied following Mr Trump's rally, and supporters and opponents met in the streets, jeering and heckling each other
Dozens of police officers in riot gear had been deployed to separate them.
Some protesters scaled a wall of the centre to throw water bottles at police.
After ordering the crowds to disperse, police then moved them away from the city's Gaslamp Quarter.
San Diego's population is about one-third Latino and hundreds of thousands of people cross the border with Mexico legally each day.
One San Diego protester, Martha McPhail, told the local City News Service: "I am opposed to the hateful, bigoted, racist language of Donald Trump and his arrogance and intolerance.
"I'm for all of our people - all races, sexes, genders, military veterans - and he's divisive."
But Trump supporter Riley Hansen defended the controversial businessman.
"My Dad always told me you need a businessman as president. I like his policies," he told CNS.
The San Diego Police Department said that 35 arrests had been made and there was no damage to property and no injuries reported.
Mr Trump tweeted to the police after the event: "Fantastic job on handling the thugs who tried to disrupt our very peaceful and well attended rally."
Mr Trump told an earlier rally in Fresno that California had "no drought", despite the state seeing its driest ever four-year period.
After speaking to farmers who complained of a lack of water for crops, he said: "They don't understand, nobody understands it. There is no drought. They turn the water out into the ocean."
The reference appeared to be about water discharged from the Sacramento River into the San Francisco Bay, partly to protect endangered species.
Mr Trump said that if he came to power he would "start opening up the water" and ensure farmers had enough for crops.
The comments sparked some mockery on social media - a number of tweets carried links to Charlton Heston in his role as Moses parting the Red Sea in the 1956 film The Ten Commandments.
Mr Trump is running unopposed in California after his Republican rivals pulled out and he reached the number of delegates needed to secure the nomination. It has yet to be formalised.
Earlier on Friday, Mr Trump backed out of an offer to debate with Democratic candidate Bernie Sanders.
"As much as I want to debate Bernie Sanders - and it would be an easy payday - I will wait to debate the first place finisher in the Democratic Party, probably Crooked Hillary Clinton, or whoever it may be," the Trump campaign said in a statement.
Mr Sanders told reporters on the campaign trail that he hoped Mr Trump would change his mind.
"Well Mr Trump, what are you afraid of?" he said, calling the Republican nominee a "bully".
Mr Trump said the Democratic nominating process was "rigged" - and that Mrs Clinton and Democratic National Committee Chairwoman Deborah Wasserman Schultz would not allow Mr Sanders to win the nomination.
The latest opinion polls suggest Mrs Clinton leads Mr Trump by about four percentage points.