Three of the injured were members of MSF, and two are in critical condition, the group said.
Several buildings collapsed and people may still be trapped in the rubble, according to MSF, also known as Doctors Without Borders.
"According to our staff on the ground, at 9.20am one projectile impacted the Shiara Hospital in Razeh district, where MSF has been working since November 2015," according to the statement.
"MSF cannot confirm the origin of the attack," the statement said.
Yemen has become a proxy battleground for Saudi Arabia and Iran.
Yemen's minority Houthis, who are Shiite, began rebelling last year against the Sunni-led government of President Abdu Rabu Mansour Hadi, which is backed by Saudi Arabia.
MSF said all warring parties, including the Saudi-led coalition, know the GPS coordinates of medical facilities in Yemen where MSF doctors practice.
"There is no way that anyone with the capacity to carry out an airstrike or launch a rocket would not have known that the Shiara Hospital was a functioning health facility providing critical services and supported by MSF," said Raquel Ayora, MSF director of operations.
"Bombing hospitals is a violation of international humanitarian law," she said.
The 10 months of war and "constant bombing" have severely affected the population of the Razeh district, MSF said.
In October, a U.S. airstrike at an MSF hospital in Afghanistan killed 30 people, including staff and patients. The U.S. apologized to MSF
and said the airstrike in Kunduz was accidental
, the result of military personnel inadvertently aiming at the wrong target -- the hospital compound -- instead of a nearby site from which Taliban fighters believed to be firing.