The graffiti was spray-painted on the front gate of James' house. Investigators are looking for any possible suspect involved, Los Angeles police spokeswoman Norma Eisenman said.
Eisenman declined to specify the racial slur used. It was reported to police shortly after dawn on Wednesday and has since been painted over, she said.
"No matter how much money you have, no matter how famous you are, no matter how many people admire you, being black in America is tough," James, a three-time NBA champion, told reporters when asked about the incident at a news conference in Oakland, California, where he is preparing for the NBA Finals.
"And we've got a long way to go for us as a society and for us as African-Americans until we feel equal in America," he added.
James was not at his west Los Angeles residence at the time of the vandalism, Eisenman said by phone.
James, 32, is the National Basketball Association's most prolific playoff scorer and has been named the league's Most Valuable Player four times. The Cavaliers are scheduled to face off on Thursday against the Golden State Warriors in Oakland.
Mary Kay Wulf, who lives a couple houses away from James, told a group of reporters that she was appalled by the vandalism.
"I hope that they find the people who have done it and they label it for what it was - a hate crime - and punish them," Wulf said.
Police are investigating the graffiti as an act of vandalism and have not determined whether to treat it as a hate crime, another Los Angeles police spokeswoman, Irma Mota, said by phone.
(Reporting by Alex Dobuzinskis and Alan Devall in Los Angeles; Editing by Alistair Bell and Leslie Adler)
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