The forces conducted their first training at Tariq bin Ziyad military base on Sunday, the ministry said.
The exercises, which had been long planned, are part of a mutual agreement aimed at strengthening the defence capabilities of both countries, as well as boosting efforts to combat armed groups and maintaining stability in the region.
The drills come as Saudi Arabia, the United Arab Emirates (UAE), Bahrain, Egypt and a number of other countries severed relations with Qatar last week, accusing it of supporting "terrorism" and Iran. Qatar rejects the accusations.
Earlier this month, Turkey's parliament fast-tracked the approval of a separate agreement with Qatar that allowed troops to be deployed to a Turkish military base in the Gulf state.
Turkey has been the foremost supporter of Qatar since the Gulf dispute began on June 5.
Ankara has also been trying to mediate between the sides in order to find a solution to the crisis.