Oliver will take leave from the Demons for the rest of the week.
"Clayton has had a difficult week personally," Melbourne's football manager Alan Richardson said.
"And as such, both he and the club have agreed that it would be best for him not to play against the Eagles on Saturday.
"We expect Clayton to return to the program next week, but as always his mental and physical health will be the priority.
"As an industry, it's pleasing to see the progress we've made in normalising players putting their hand up when they need support.
"The club's focus is on surrounding Clayton with the care he needs and we ask that his privacy is respected."
Oliver played just seven games last season while dealing with personal issues and was shopped for a trade, with Geelong keen.
But the Demons then stood firm in keeping the four-time club champion.
After five losses to start their season, Melbourne have downed Fremantle and Richmond but coach Simon Goodwin is wary of the Perth trip to meet the winless Eagles at Optus Stadium.
Last year, Melbourne suffered a shock 35-point loss to West Coast at the venue in round 11 and returned to lose by 50 points to Fremantle in round 20.
"Clearly our performances last year in Perth, both against West Coast and Fremantle, weren't to the level," Goodwin said.
"We've been working really hard on our style of play over the last month and how we show up week after week.
"We want to be a team that is really hard to play against, no matter where or who we're playing."
The Demons travel following the long-awaited appointment of a new chief executive officer. Paul Guerra.
"He comes from a great background, has enormous experience and I think he's going to provide great stability," Goodwin said.
"I've only had a really brief conversation with him but it has certainly been one of support and about working on how we generate a really high-performing footy club."
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