The airport has been a major conduit for aid flights since a February 6 earthquake devastated swathes of southeastern Turkey and neighbouring Syria, and they too were brought to a stop, a transport ministry official said.
Flights, including those carrying aid, have been diverted to the Damascus and Latakia airports, the ministry said.
"At exactly 2:07 am (2307 GMT Monday), the Israeli enemy carried out an air attack from the Mediterranean west of Latakia targeting Aleppo international airport," Syria's defence ministry said in a statement.
The damage forced authorities to close the airport to all flights, the ministry added. There was no immediate word on any casualties.
More than 80 aid flights have landed in Aleppo over the past month with relief supplies for quake-hit areas, transport ministry official Suleiman Khalil told AFP.
"It is no longer possible to receive aid flights until the damage has been repaired," he said, adding that the strike had put the runway out of service.
An Israeli military spokesperson declined to comment on the reported strike.
It marked the second Israeli attack on regime-held areas since the devastating quake struck Turkey and Syria, killing more than 50,000 people in the two countries.
On 19 February, an Israeli strike killed 15 people in a Damascus district housing state security agencies.
Israel has attacked Aleppo airport several times in recent years, with a strike last September putting it out of service for a few days.
Since civil war erupted in Syria in 2011, Israel has carried out hundreds of air strikes against its neighbour, primarily targeting positions of the Syrian army and its Iranian and Hezbollah allies.
The Israeli military rarely comments on individual strikes against Syria but has vowed repeatedly to keep up its air campaign to stop arch-foe Iran from consolidating its presence.