The airport was being used to deliver aid to victims of last month's earthquake that killed thousands.
U.S. State Department spokesperson Ned Price said that, while he could not "speak to attribution" for Tuesday's air strike, Washington would worry about any lengthy halt to the flow of humanitarian aid.
He said all U.N. Humanitarian Air Service (UNHAS) flights from Aleppo had been suspended, adding that those flights transport aid workers and life-saving supplies and must resume without delay.
The Israeli military declined to comment on the Syrian state media accusation that it was behind the air strike.
Foreign donors including the United Arab Emirates, Iran, Saudi Arabia and Algeria have flown aid into Aleppo airport since the Feb. 6 earthquake, Syrian state media has reported.