The damage caused by Tuesday's raid forced aid deliveries and all flights to be diverted to Latakia and Damascus airports, the transport ministry had said.
"The airport has been operational since 8 his morning the morning (0500 GMT). We repaired all the damage," ministry official Souleiman Khalil told AFP on Friday.
However, "no civilian planes are scheduled to land in Aleppo airport today", an airport official said, speaking on condition of anonymity because he is not allowed to talk to the press.
Israeli warplanes killed three people in the raid on the airport in Aleppo, Syria's second city, the Syrian Observatory for Human Rights war monitor had said.
Before that more than 80 aid flights had landed there with relief supplies following the devastating earthquake that killed more than 50,000 people in Syria and Turkey, Khalil had said at the time.
The United Nations' resident Syria coordinator El-Mostafa Benlamlih said in a statement on Wednesday that he was "deeply concerned" about the airport closure.
"The impact of this closure impedes humanitarian access and could have drastic humanitarian consequences for millions of people who have been affected by the earthquake," he added.
Tuesday's Israeli raid was the second of its kind since the 7.8 magnitude quake struck Syria and Turkey.
On February 19, an Israeli air strike killed 15 people in a Damascus district housing state security agencies, the British-based Observatory had said.
Israel has attacked Aleppo and Damascus airports several times in recent years, killing dozens pf Syrians and injuring scores more. However, Israel rarely comments on individual strikes against Syria.
It has, however, vowed to keep up its air campaign against Syria to stop arch foe and Damascus ally Iran from consolidating its presence there.
Since Syria's civil war erupted in 2011, Israel has carried out hundreds of strikes against its northern neighbour, targeting government troops as well as allied Iran-backed forces and Hezbollah fighters.