The maximum punishment for a second-degree manslaughter conviction is 10 years in prison, though sentencing guidelines call for about four years for someone with no criminal history.
The planned charge against the officer, Kimberly A. Potter, was announced a day after she and the police chief both resigned from the Brooklyn Center Police Department.
In a police video of the shooting, Potter shouts, "Taser, Taser, Taser!" as she pulls her weapon and opens fire on Wright in his auto after he had just scuffled with a fellow officer, then she is heard to say, "H**y s**t, I just shot him".
Brooklyn Center Mayor Mike Elliott had said he hoped Potter's resignation would "bring some calm to the community", but that he would keep working toward "full accountability under the law".
"Michelle and I grieve alongside the Wright family for their loss", Mr Obama said in the statement.
Wright's family have said they can not accept the theory that his death was an accident.
Potter is at least the third USA law enforcement officer to face charges after claiming they mistakenly killed someone with a gun when they meant to use a Taser.
"Certain occupations carry an enormous responsibility and none more so than a sworn police officer", Imran Ali, assistant criminal division chief and director of the major crimes unit for the County Attorney's Office, said in the statement.
Police said Wright was first pulled over by the officers for expired license plate tags. "Taser! Taser!" before firing a single shot from her handgun. Mehserle testified at trial that he mistakenly pulled his.40-caliber handgun instead of his stun gun.
In a press conference on Wednesday, Wright family attorney Ben Crump and Rev. Al Sharpton praised Orput's quick action to charge Potter - but Sharpton added that he felt a second-degree manslaughter charge was the "least" charge that Potter should face.
Meanwhile, Wednesday night demonstrators gathered for a fourth night outside a police station in Brooklyn Center. Dozens of police officers in riot gear, along with National Guard members, stood on the other side of a large metal fence erected around the perimeter of the station earlier this week. Several hundred protesters filled the street in front of the station despite a mix of snow and rain, chanting "Say his name!"
He did not know whether an unlawful assembly had been declared or whether any protesters had been arrested.
Shortly before the dispersal order, some protesters threw objects at police, who responded with occasional gas canisters. Protesters near the fence formed a wall with umbrellas. After Floyd's death past year, protesters demonstrated several times at the home of Derek Chauvin, the former Minneapolis officer now on trial in Floyd's death. Today, a majority of residents are Black, Asian or Hispanic.
Elliott said Tuesday that he didn't have at hand information on the police force's racial diversity but that "we have very few people of colour in our department".