In a statement, the US said it was an "extra-judicial release" of detainees that would be "a major step backwards".
The detainees are part of a group of 88 prisoners previously held by the US but handed to Afghan control in 2013.
The US insists they are "dangerous individuals" but Afghanistan says there is not enough evidence against them.
Earlier this month, the Afghan government announced it would release 72 out of the 88 prisoners, prompting almost instant condemnation from the US  which said there was "strong evidence" linking the 72 to "terror-related crimes".
Hundreds of prisoners at Bagram jail have been freed since the Afghan government took over the running of the prison in March last year.
But it is the fate of these 88 detainees which has proved so controversial.
Of the 72 prisoners it plans to free, the Afghan government says there is no evidence against 45, while the evidence against 27 others is not enough to put them on trial.
But the US has said any releases would constitute a breach of a memorandum of understanding agreed between the two sides at the time the US handed over control of Bagram jail, where these prisoners were held.
"The ARB [Afghan Review Board] is releasing back to society dangerous insurgents who have Afghan blood on their hands," Monday's statement from the US military said, on learning that a release order had been granted for 37 of these men.
It went on to say that among the 37 are 17 who are linked to bomb attacks and others who had knowledge of or were directly involved in attacks which wounded or killed Afghan and coalition soldiers.
The two countries have been at loggerheads over President Hamid Karzai's refusal to sign a security deal with Washington that would set the final framework for the US withdrawal from Afghanistan.
According to the UN Security Council's mandate, the US-led international military force in Afghanistan is scheduled to hand over all security duties to Afghan forces before its full withdrawal by the end of 2014.
But if a "Security and Defence Co-operation Agreement" is signed between the two countries, about 10,000 US troops could stay in Afghanistan for another 10 years.
The US military has condemned an order  by the Afghan government to release 37 prisoners deemed by the Americans to pose a threat to security.