A statement says the soldiers and their interpreter were killed Monday in Diyala province.
Diyala is an area north of the capital that continues to be volatile despite an overall drop in violence nationwide.
At least 4,250 members of the U.S. military have died in the Iraq war since it began in March 2003, according to an Associated Press count.
In other news:
The ransacking of the museum became a symbol for critics of Washington's post-invasion strategy and its inability to maintain order as Saddam Hussein's police and military unraveled.
But Iraq's prime minister, Nouri al-Maliki, chose to look ahead. He called the reopening another milestone in Baghdad's slow return to stability after years of bloodshed.
"It was a dark age that Iraq passed through," the prime minister said at a dedication ceremony after walking down a red carpet into the museum. "This spot of civilization has had its share of destruction."
Spokesman Maj. Gen. Abdul-Karim Khalaf says the 12 people arrested were former employees of the ministry. The Interior Ministry has been accused of past infiltration by Shiite militias who perpetrated some of the worst sectarian violence.
Khalaf said Monday at a press conference that the suspects are accused of killing the sister of Vice President Tariq al-Hashemi.
Maysoun al-Hashemi died in a hail of gunfire on April 27, 2006, as she left her home in Baghdad.
Khalaf says the suspects include 11 police and one civilian ministry employee. They're accused in a total of 15 criminal operations.