The donation was made on behalf of the Roman Curia at the end of the pontiff's Lenten retreat in Ariccia - on the outskirts of Rome - last week.
Fr Ibrahim Alsabagh, a parish priest in Aleppo, told Italian radio station InBlu that the donation is a "sign of hope for us".
The priest also said that young couples continue to suffer from hunger and poverty amid Syria's continuing crisis.
Fr Alsabagha said the money would be used to provide the couples and others in need, with food packages and help cover bills.
The war in Syria has been raging for six years.
Syrian security forces gather in front the main judicial building where 39 people were killed by a suicide bomber in Damascus
On Wednesday, 39 people were killed in a suicide bombing outside a judicial building in Damascus.
Unicef said the last year of the conflict has been worse for Syrian children than the other five, with 652 killed.
Officials estimates suggest more than 400,000 people have died since 2011.