Shij'ia Clinic, run by the Near East Council of Churches (NECC) and funded by Christian Aid, was given just 15 minutes to evacuate. No one was injured in the attack but the building was completely destroyed by missiles on Saturday, along with hundreds of thousands of pounds of medical equipment.
There are also fears that a mobile dental clinic run by the NECC and funded by the Church in Wales was also destroyed.
Dr Barry Morgan said, "We find it incomprehensible and tragic that any armed forces anywhere in the world would want to destroy such a building, let alone the State of Israel with all its historic memories of oppression and genocide.
"To hear the news that the only health facilities in this part of Gaza have been destroyed, leaving the population of that area without any medical facilities at all, is horrendous.
"It does raise questions about the credibility of Israel's values and purposes."
There were 10,836 families registered at the clinic, which provided free primary health care and included a mother and baby clinic. Those families had, he said, "effectively been removed of any hope of medical provision and support."
"It is hard to understand why Israel would allow, let alone commission, an attack on a facility which provides support mostly to young babies and their mothers," he said.
"We have no reason to believe that this building was producing or distributing arms or being used as a base or launch pad for rockets sent into Israel. If there is evidence to the contrary we would like to see it."
Dr Morgan wrote to the Israeli Ambassador to London on Tuesday asking why Israel had attacked the Shij'ia Family Health Care Centre in Gaza City.
"We are perplexed and shocked at this attack and are looking for an explanation for it from the Israeli Ambassador," he said.
Constantine Dabbagh, Executive Director of the Near East Council of Churches, called on the international community to act.
