The 20,000 seat venue has mandated that all vendors not serve "flesh as food" that evening and, at the request of the singer, the McDonald's concession will not open.
The singer said in a statement "I don't look upon it as a victory for me but a victory for the animals."
The Staples Center will also donate a portion of the ticket sales to PETA.
The singer recently postponed three additional shows while being treated for a bleeding ulcer and Barrett's Esophagus. He has vowed to be back in shape for a February 26 Jimmy Kimmel show appearance and the March 1 show.