"He is not going to be with the team," Mariners general manager Jack Zduriencik told Major League Baseball's website (www.mlb.com).
"When he goes back to join the team, he will be ready to play."
Bradley, in the second year of a three-year, $30 million contract, asked for help on Wednesday, a day after he was pulled from the lineup following an angry exchange with manager Don Wakamatsu.
The confrontation occurred after Bradley, who has a history of run-ins with fans and team mates, struck out with the bases loaded.
Players on baseball's restricted list do not receive pay and may not sign with another team.
Zduriencik would not say how long Bradley might be out. The mercurial outfielder is hitting just .214 this season, well below his .276 lifetime average.
"It's better to say that the process has started," Zduriencik said.
The Mariners, mired in a six-game losing streak, have a three-game home stand against the Los Angeles Angels this weekend, then begin a road trip to Baltimore, Tampa Bay and Oakland before returning home on May 19.
"We will see where we are that time," Zduriencik said.
(Reporting by Gene Cherry in Raleigh, North Carolina; Editing by Steve Ginsburg)