At least 22 people, including MSF staff, were killed in attacks the charity blames on US-led NATO forces.
MSF said it was making the call for an inquiry “under the clear presumption that a war crime has been committed”.
The US military says it is investigating the incident.
Twelve MSF staff members and 10 patients were killed when the hospital was hit as Afghan government forces, backed by the US-led coalition, battled to retake the northern city from Taliban fighters.
Dozens were injured and the hospital severely damaged by a series of airstrikes lasting more than an hour from 02:00 local time on Saturday morning, October 3.
On its Twitter feed, MSF said: “The hospital was repeatedly and precisely hit during each aerial raid, while the rest of the compound was left mostly untouched.
“Not a single member of our staff reported any fighting inside the hospital compound prior to the US air strike on Saturday morning.”
Afghan troops are now reported to have recaptured most of Kunduz, six days after it was seized by the Taliban.
MSF said it was pulling most of its staff out of the area but some medical staff was treating the wounded at other clinics.
“The MSF hospital is not functional anymore. All critical patients have been referred to other health facilities and no MSF staff are working in our hospital,” a spokeswoman for the charity told AFP.
“I can’t confirm at this stage whether our Kunduz trauma centre will reopen, or not,” she added.
MSF says the hospital was a lifeline for thousands in the city and in northern Afghanistan.
President Barack Obama has expressed condolences and says the US has launched a “full investigation” into the incident which happened on Saturday. He said he would await the results of the inquiry before making a definitive judgement.
The US military said a strike targeting Taliban in Kunduz may have caused “collateral damage”, and that the results of a multinational preliminary investigation would be available “within days”.
“Additionally, the US military has opened a formal investigation… to conduct a thorough and comprehensive inquiry,” it added.
The UN called the strikes “inexcusable and possibly even criminal”, with Secretary General Ban Ki-moon calling for a thorough and impartial investigation.
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