Kushner was traveling with General Joe Dunford, chairman of the Joint Chiefs of Staff, who had invited him, the official said.
Additional details of the trip were not immediately available, though the fight against the Islamic State group was sure to top the agenda.
The United States is leading an international coalition fighting the IS group, launching air strikes to assist Iraqi forces on the ground.
Since last month, the forces have been engaged in a grinding battle for west Mosul, sending more than 200,000 civilians fleeing for safety.
Kushner, like his father-in-law, has no previous experience in government but has risen stratospherically to become one of the most powerful men in Washington.
Valued by Trump for his discretion and loyalty, the baby-faced 36-year-old is officially a White House senior adviser with far-reaching influence over domestic and foreign policy.
His wife Ivanka, the 35-year-old first daughter, also plays a key role in advising the president.
She officially became assistant to the president last week, after being a regular presence in the White House since Trump's election.
