The comedian is said to be concerned that Beckham will "kick off" over his treatment of her fellow Spice Girl Geri Halliwell.
Brand and Halliwell started a brief fling at the end of last month, but the romance lasted 13 days before he was spotted with other women.
"Russell's avoiding Posh at all costs. He's scared to visit the places where he used to bump into her," a source told the Daily Star.
"It's got so bad he's even changed his regular coffee shop because she goes there, and now goes to one that's two miles from his home in west Hollywood.
"He knows he didn't treat Geri too kindly, and is convinced Victoria will kick off when she sees him."
Brand was most recently spotted kissing a mystery woman outside his yoga class in LA.