The investigation will also assess the future of the contested Monywa project in northern Burma.
The 30-strong non-parliamentary commission will investigate the "social and environmental issues" behind the protests, which include allegations of mass evictions to make way for the mine.
The Nobel laureate has sought to mediate an end to the stand-off at the mine, which saw scores of villagers and monks injured in the toughest clampdown on demonstrators since president's reform-minded government came to power last year.
Photographs of the protesters' injuries, which included severe burns, have stirred outcry across Burma.
Apology for monks
The commission will "investigate the truth" of the pre-dawn raid by riot police and assess whether the "copper mining project is being implemented in accord with international norms", said a statement on the presidential office website, signed by Thein Sein.
It will also advise whether "to continue the copper mining project and whether to stop foreign investment", the statement said, without providing further details.
Activists are calling for work at the mine - a joint venture between Chinese firm Wanbao and military-owned Myanmar Economic Holding - to be suspended to allow impact studies amid allegations of mass evictions and pollution.
China insists that the contentious points had already been resolved, but the dispute echoes fierce opposition to a Chinese-backed dam which saw President Thein Sein order the scheme's suspension last year in response to public anger.
Ms Suu Kyi visited the area and on Friday and demanded an apology for monks hurt in the crackdown, after holding talks with both sides.
But the veteran dissident struck a conciliatory tone towards China and declined to back calls for an immediate halt to work on the mine.
In a renewed sign of growing anti-China sentiment around 50 people marched to the Chinese Embassy in Rangoon on Saturday.
The presidential office statement followed an apology by police for injuring monks in their crackdown on protest camps on Thursday, but tensions over the pre-dawn raid remained high.
A senior police official among around 100 officers told a group of 10 monks that "we are sorry for what happened and apologise", according to the AFP reporter at the scene, although it was unclear if the monks accepted the apology.
Phil Robertson, deputy Asia director at US-based Human Rights Watch, had called for a speedy official investigation.
"A hospital ward full of horribly burned Buddhist monks and other protesters deserve to know who attacked them while they were sleeping and what the government is going to do about it," he said in a statement.
"The crackdown...is a fundamental test case for the government's commitment to peaceful assembly and willingness to demand accountability for abuses."
Anger has been growing at the heavy-handed police intervention at the mine, reminiscent of the way dissent was stifled under the junta that ruled Burma for half a century.
Local residents say the $1 billion mine expansion entails the unlawful confiscation of more than 3,160 hectares of land.