The videos appeared genuine and corresponded to Associated Press reporting of the events.
The Britain-based Syrian Observatory for Human Rights, which covers the conflict through a network of activists on the ground, said at least 19 people were killed in the strike, including 10 children. The local Aleppo Media Center put the toll at 25 killed, most of them children.
The United Nations Children's Fund said in a statement it was "outraged by the latest wave of indiscriminate attacks perpetrated against schools and other civilian targets across Syria."
Thousands of Syrian children have been killed in Syria's 3-year-old conflict, which began as an uprising against Assad's rule, but has become a civil war that has killed more than 150,000 people and displaced millions.
Parts of the two-story Ein Jalout school appeared to have been completely smashed, according to the videos, which showed blood splatters, twisted metal and children's items, like a little red heart-shaped box. A man speaking in one of the videos said the exhibition was for drawings by children from schools around the area.
An opposition activist from Aleppo now based in Berlin provided the AP with a copy of the invitation to the exhibition to confirm it was taking place. Mohammed Neser, the activist, said he feared that his colleagues who organized the show were now dead.
"I haven't been able to get in touch with them," he said.
Aleppo, Syria's largest city, has been divided between government forces and rebels for nearly two years, with constant fighting doing little to change the balance on the ground. Forces loyal to Syrian President Bashar Assad have been carrying out airstrikes and dropping crude barrel bombs in rebel-held districts in the eastern part of the city, at times hitting schools, mosques and markets.
Rebels have hit back with mortar strikes and car bombs.
Mortar fire also killed three people near the Central Prison complex in Damascus, state news agency SANA said. A day earlier, a mortar strike in Damascus and a double car bombing in the central city of Homs killed at least 54 people.
In a statement Wednesday, U.N. Secretary-General Ban Ki-moon condemned those attacks, calling them "horrendous acts of terror against innocent civilians."
At the United Nations, members of the Security Council said they fear that no progress will be made on getting desperately needed humanitarian aid into Syria as long as Russia opposes any actions against Assad's government. Moscow has been a staunch ally of Damascus throughout the three-year-old conflict. The U.S. and its European and Gulf Arab allies are backing the opposition.
The U.N. estimates almost 3.5 million civilians inside Syria have virtually no humanitarian aid access. Millions of others suffer because of food and medicine shortages. Ban Ki-moon has criticized both rebel and government forces for blocking efforts to get aid into the country.
Also Wednesday, another six Syrians submitted their candidacy applications to run in presidential elections slated for June 3, bringing the number of contenders so far to 17, Parliament Speaker Jihad Laham said.
Assad announced earlier this week that he will run for re-election. The others who are seeking to run are not well-known.
In a televised campaign-style appearance Tuesday, Assad and his wife Asma met with parents who lost their only sons in the conflict.
Opposition activists and Western countries have condemned the elections as a sham. Assad is widely expected to win his third seven-year term since coming to power in 2000, and the vote is seen as an attempt to give him a veneer of electoral legitimacy amid the war.
Associated Press writer Cara Anna at the United Nations contributed to this report.