The department calls the incident "a flagrant violation of all national laws and conventions" that prescribe the protection of healthcare facilities and patients.
The detained Palestinian is from the vicinity of Tubas on the northern West Bank and was a target of an Israeli attack on Tuesday, which according to Israel killed three other Palestinians. The man was injured in the attack.
Israel confirms in a statement that they have arrested the man at the hospital. The man is accused of being "the third member of a terrorist cell" that carried out a shooting in Mehola in August, in which an Israeli died.
Earlier reports also emerged about Jewish settlers carrying out a series of attacks on Palestinian towns on the West Bank during the night leading up to Wednesday.
The settlers allegedly burned down homes and clashed with Israeli soldiers. There are no reports of Palestinian fatalities.
According to the Israeli military, settlers attacked the village of Beit Furik after soldiers arrived in the area to dismantle unauthorized farming.
The settlers threw stones and injured two members of the paramilitary border police, and a group entered the village and set property on fire.
On the West Bank, violence from settlers has increased significantly since the war between Israel and Hamas, which is labeled as a terrorist organization, began in Gaza.