The exercises come as Ankara presses on with its unequivocal backing of Doha in the crisis triggered by the political and economic isolation of Qatar by Gulf and other Arab states led by Saudi Arabia.
Turkish state media said that the Turkish frigate TCG Gokova had docked in Doha earlier this week carrying 214 soldiers who would take part in the exercises.
The exercises got underway on Tuesday and would intially involve ground forces with naval forces later on, NTV television said. An observation day involving top commanders would take place on August 7-8, it added.
A total of 250 Turkish soldiers and 30 armoured vehicles will take part, it added.
On June 5, Saudi Arabia, Bahrain, the United Arab Emirates and Egypt cut ties with Qatar accusing it of backing extremism and fostering ties with their Shiite rival Iran.
Doha denies the claims and has been strongly backed by Ankara throughout the standoff.
The crisis has put Turkey in a delicate position as it seeks to balance its strategic alliance with Qatar with preserving its own relations with regional kingpin Saudi Arabia.
Turkey is setting up a military base in Qatar, its only such outpost in the region. It has sped up the process since the crisis began and reportedly now has 150 troops at the base.
After a whistlestop tour of the region last month that included visits to Qatar, Saudi Arabia and Kuwait, Turkish President Recep Tayyip Erdogan said more time was needed to solve the crisis.