At least 22 staff and patients were killed in the bombing in the city of Kunduz a week ago.
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 Defence 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 Obama has apologised 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.
The Pentagon is to pay compensation for those killed and injured in a US strike on a Medecins Sans Frontieres (MSF) hospital in northern Afghanistan.