It was not immediately clear how authorities located the suspect.
Holder, of Los Angeles, was previously identified by Los Angeles police as the suspect in the case.
"We believe this to be a dispute between Mr. Hussle and Mr. Holder, " Moore said. LAPD says Holder approached Nipsey on multiple occasions Sunday and engaged him in conversation regarding personal dispute.
The suspect then allegedly ran to a getaway auto, driven by an unidentified woman.
The panic came about 8:15 p.m., Moore said, and "as (the crowd) fled, we had a series of falls and trips and injuries".
"I ask for you to bring peace and not allow this sacred ground to be the site of any further violence", Moore said.
Mayor Eric Garcetti at the same news conference announced plans to deploy new resources to try to roll back the violence.
Surveillance video reportedly captured the scene outside the rapper's clothing store.
APEric Holder and Nipsey Hussle are said to have known each other
Both Moore and Police Commission President Steve Soboroff said they were devastated when they learned Hussle had been killed on the eve of their talk. Soboroff on Tuesday morning read for reporters the email he received from Hussle in February requesting the meeting.
A tense scene unfolded Monday night at an impromptu memorial for Hussle in the parking lot where he was shot.
The Los Angeles Times said several people were stabbed after a fight broke out at the vigil and two people were in a critical condition.
According to The Blast, authorities have taken a man named Eric Holder into custody on the suspicion that he may have been the one to pull the trigger and end Hussle's life. Two other men were shot as well, however their wounds were not life-threatening.
"It's been a tough few days for Los Angeles", Garcetti said.
Before his death, Nipsey and Lauren opened up about their relationship in a joint interview, where the model admitted that their own versions of how they met didn't exactly parallel one another.
The Los Angeles County coroner's office confirmed the rapper - who was born Ermias Joseph Asghedom - died of gunshot wounds to the head torso.