More than 70 people were killed at the building which sheltered displaced Palestinians, the director of a hospital has told the BBC.
Ms Harris said "far too many" civilians had been killed "yet again"and reiterated calls for a hostage deal and a ceasefire, echoing comments made by the White House.
An Israeli military spokesman said al-Taba’een school "served as an active Hamas and Islamic Jihad military facility", which Hamas denies.
Speaking at a campaign event in Phoenix, Arizona, Ms Harris said Israel had a right to "go after Hamas" but also has "an important responsibility" to avoid civilian casualties.
Saturday's air strike has been criticised by Western and regional powers, with Egypt saying it showed Israel had no desire to reach a ceasefire or end the Gaza war.
Fadl Naeem, head of al-Ahli Hospital where many of the casualties were taken, said around 70 victims were indentified in the hours after the strike - with the remains of many others so badly disfigured that identification was difficult.
Israel's military said it had "precisely struck Hamas terrorists operating within a Hamas command and control centre embedded in the al-Taba'een school".
A statement by the Israel Defense Forces (IDF) and the Israeli Security Agency said "at least 19 Hamas and Islamic Jihad terrorists" were "eliminated" in the attack.
