"We are deeply appalled by the verdict of the Fairfax court in the state of Virginia. We consider it to be reprehensible and unprecedented, even if in this case, unlike in several previous cases, it was criminal negligence that led to the tragedy rather than intentionally cruel treatment," the ministry said in a statement.
Harrison, 49, was acquitted on Wednesday of the involuntary manslaughter of his 21-month-old son Chase (born Dmitry Yakolev), who died of heatstroke in July after he was accidentally left for nine hours in a vehicle parked in the sun outside his adoptive father's workplace in Virginia.
"We will demand that U.S. authorities review the extremely unfair ruling. Further cooperation with the United States in adoption will depend on Washington's readiness to take practical steps to ease our concerns," the ministry said.
The statement came after criticism earlier on Thursday by a senior Russian education and social protection official, who said adoption requirements for U.S. nationals would be toughened following the acquittal.
Explaining the ruling, Fairfax County Judge R. Terence Ney said Harrison's conduct did not meet the legal standard for manslaughter, which requires "negligence so gross, wanton and culpable as to show a callous disregard for human life."
"No prison term is going to cause more pain than that which he has already suffered. The only true atonement here can only take place within his heart and soul," the judge said.
Over the last 10 years in the United States there have been approximately 230 fatal cases of parents locking their children in cars on a hot day.
Several calls for tighter controls on adoptions have been made in Russia in recent years over a series of scandals, notably the killing of a 2-year-old girl from Siberia by her adoptive mother in the United States. The woman, Peggy Sue Hilt, was sentenced to 25 years in prison in May 2006 for beating the child to death.