Among the fatalities in the early Saturday morning attack were three children. It also wounded 37 people, including 19 MSF staff, the medical charity said.
In a statement on Saturday, the office of President Ashraf Ghani said Army General John Campbell, head of the US-led forces in Afghanistan has apologised for the incident.
Officials of MSF earlier told Reuters that they "frantically phoned" NATO and Washington DC, as bombs rained on the hospital for "nearly an hour".
Pentagon has also acknowledged launching the air strike "against individuals threatening the force".
"The strike may have resulted in collateral damage to a nearby medical facility. This incident is under investigation."
Earlier, NATO said that a US air strike "may have" hit the hospital, which is run by the medical charity, adding that the attack may have resulted in collateral damage.
The MSF hospital is seen as a key medical lifeline in Kunduz, which has been running "beyond capacity" in recent days of fighting which saw the Taliban seize control of the provincial capital for several days.
The trauma centre is the only medical facility in the region that can deal with major injuries.
"At 2:10 am (20:40 GMT) local time ... the MSF trauma centre in Kunduz was hit several times during sustained bombing and was very badly damaged," MSF said in a statement on Friday.
At the time of the bombing, 105 patients and their caretakers and more than 80 MSF international and national staff were present in the hospital, the charity said.
