Dozens of others were seriously wounded at the facility, a key medical lifeline that has been running "beyond capacity" during recent fighting that saw the Taliban seize control of the northern provincial capital for several days.
The strike early today left the building engulfed in flames, with photos posted on Twitter by Doctors Without Borders showing shocked and dazed staff in the aftermath of the bombing.
"It is with deep sadness that we confirm so far the death of nine MSF staff during the bombing... 37 people were seriously wounded... There are many patients and staff who remain unaccounted for."
It said the bombing continued for more than 30 minutes after American and Afghan military officials in Kabul and Washington were first informed.
"All parties to the conflict, including in Kabul and Washington, were clearly informed of the precise location (GPS coordinates) of the MSF facilities," the statement added.
NATO conceded that US forces may have been behind the strike but has not so far commented on MSF's specific claims.
"US forces conducted an air strike in Kunduz city at 2:15 AM (local time)... Against individuals threatening the force," a NATO statement said.
"The strike may have resulted in collateral damage to a nearby medical facility. This incident is under investigation."
Today's bombing came after Taliban insurgents overran the northern Afghan city on Monday. It was the first major city to be captured by militants since 2001.
MSF said some 105 patients and their caregivers, as well as more than 80 international and local MSF staff were in the hospital at the time of the bombing.
