Due to the bombings of health centers that are taking place in the civil conflict, the city's Saudi hospital has been hit twice since the fighting began.
On the other hand, this is the eighth hospital unit to be hit in the last six weeks of the conflict, MSF said in the statement.
El Fasher is the last stronghold of Sudanese army troops in Darfur, western Sudan.
Two weeks ago, the Southern hospital, also in El Fasher, was closed after being attacked for the fifth time and, before that, the local pediatric hospital was also closed following the exchange of offensives between the Rapid Support Forces (RSF ) and the Sudanese Armed Forces (SAF).
"In El Fasher, we are witnessing a cycle of offensives and counteroffensives in which hospitals are not spared and the warring parties are failing in their responsibility to protect civilians," said MSF emergency manager Michel-Olivier Lacharite.
Currently, the Saudi hospital - formerly a maternity ward - has become the "only health center in the city with surgical capacity to treat the injured", but its continuity "is in danger", warned Michael-Olivier Lacharité in the statement.
The organization stated that, ten days after the UN called for an end to the fighting in El Fasher, attacks on hospitals continue and "foreign aid" is unable to arrive due to the "brutality" of armed violence.
MSF says it does not know whether hospitals are being "deliberately targeted", but as a result of the violence of the open conflict, many civilians are trapped and have to "protect their lives and receive treatment".
MSF data indicates that fighting over the last six months has caused more than 260 deaths and 1,630 injuries in El Fasher alone.
