The facility in Saada, a stronghold of the rebel Houthi movement in north-western Yemen, was hit on Friday.
UN Secretary General Antonio Guterres said in a statement that the "escalation needs to stop".
In a statement on Saturday, the Saudi-led coalition fighting Houthi rebels in the country denied it had carried out the air strike.
The coalition also said the site was not on a list of targets to avoid that had been agreed with the UN and had not been reported by the Red Cross.
