The Facebook post shows the First Couple in what appears to be a hospital environment, with the First Lady placed on a drip as her embattled husband sits beside her in support.
"With strength, trust and faith".
The announcement is unusual, as cancer is considered a taboo in the Arab world.
The 42-year-old Asma Assad is originally from the central province of Homs.
An investment banker before she quit her job following her marriage to President al-Assad in 2000, Asma was born and raised in London before moving back to Syria after meeting the president.
Since Syria's civil war broke out, Mrs Assad has mostly been seen in public receiving families of fallen soldiers, or hosting people wounded in the conflict, now in its eighth year, which has killed more than 400,000 people.
As Syria's conflict worsened, the first lady became a target of contempt for many opposition supporters who saw her as whitewashing atrocities carried out by the government.