At least 22 hospital staff and patients were killed in the bombing in the city of Kunduz last week.
The US has said the strike was a mistake and that it was trying to target Taliban insurgents.
MSF has called the attack a war crime and called for an international committee to investigate.
Those injured in the strike and the families of those killed are eligible for “condolence payments” from the US.
“The Department of Defense believes it is important to address the consequences of the tragic incident at the MSF hospital,” a Pentagon spokesman said.
Funds will also be made available to repair the hospital, the Pentagon added.
President Barack Obama has apologized to the MSF president and the Afghan leader for the incident.
MSF is still trying to trace more than 30 staff and patients who remain unaccounted for.
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