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.

Kim Thomas Riley, 27, made a getaway from Royal Darwin Hospital, where he was undergoing assessment for chest pains.
Authorities found him hiding under a log near Cape Crawford, a remote road stop in the Northern Territory outback.
Police arrested him "without incident" after a two-day search.
His partner, Rachel Chatfield, was charged with aiding his escape.
Police said she picked up Riley from the hospital and the couple drove more than 700km south to the small town of Elliot.
Riley reportedly left Ms Chatfield and her children on the side of the Stuart Highway for reasons that are not yet clear and drove several hundred kilometres east.
The car he was driving ran out of petrol at Borroloola, a remote fishing community on the Gulf of Carpentaria.
He was arrested about two kilometres away at Cape Crawford, still wearing handcuffs and with an injury to his foot.

The self-employed and those with more than one source of income must submit their self-assessment forms online by 31 January,
Data from returns made last year showed that men were most likely to file late.
Those aged between 18 and 20 and living in London were the worst offenders, the tax authority said.
So far, 6.45 million returns have been submitted ahead of the deadline at the end of the month, with about another 4.5 million outstanding.
"Whatever your gender, age, occupation or location, if you haven't sent in your 2013-14 tax return, you need to take action now. Don't leave it until the last minute to contact us. Do it now, and avoid a last-minute rush to beat the deadline," said Ruth Owen of HM Revenue and Customs.
The figures from a year ago showed that the over-65s were the most punctual.
Interestingly, lawyers and accountants were not the most punctual - with 219 late filers per 10,000 submitted. Those in agriculture, fishing and forestry were more efficient, with 109 per 10,000 filing late.

Yeovil District Hospital was put on "black alert" last year when it was overwhelmed by demand.
This year the hospital is installing a 24-bed modular ward on its roof and leasing 18 beds from a nursing home.
Chief Executive Paul Mears said: "Winter is a challenging time for us and we've taken action to ensure we're well prepared for this winter."
Last February, the hospital was put on "black alert" for two weeks as it struggled to cope with the number of people coming into its accident and emergency department.
What is a black alert?
â€¢The NHS uses a national internal alert system based on the colours green, amber, red and black to rank how busy a local health and social care system is
â€¢Black alert status occurs when a hospital cannot cope with the number of people coming into the accident and emergency department because not enough people are being discharged
â€¢It effectively means the hospital does not have enough bed capacity to cope
This year, to boost bed capacity, the hospital is hoisting a permanent emergency admissions unit onto the roof of its outpatient department in the run-up to Christmas.
It has also contracted with a local nursing home to take 18 beds for six months for patients waiting for nursing home placements or a package of care.
"Last winter was really, really bad for us - part of that was due to the complexity of the patients we were admitting which were a more elderly, frail group of patients and also the sheer numbers," said Mr Mears.
"But we've got 42 beds on top of our current bed base now and we believe that will put us in a much better place to be able to cope with the additional pressures."
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.
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A prisoner who escaped from hospital in northern Australia was rearrested about 1,000km (620 miles) away still wearing handcuffs.
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Young men working in the communications industry are the most likely to miss the looming tax return deadline, HM Revenue and Customs figures suggest.
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A "ready made" ward is to be craned onto the roof of a Somerset hospital to help cope with winter demand.