The family said that they returned to their Fairfax County apartment on Monday after a weekend away to find their apartment broken into.
The couple, Mahrukh and her husband Shoaib, asked that they be identified only by their first names.
In addition to the Quran, Mahrukh said artwork with religious calligraphy was damaged and thrown to the floor. The burglars stole the family's green cards and valuables they received as wedding gifts, AP reported.
Shoaib said the couple, who were born in Pakistan, and their two children had moved to the D.C. suburb moved last month from Dubai.
Police are investigating the burglary as a bias incident.