The suspect, who was reportedly unhappy with working conditions, was arrested after Thursday's killings at the base in the northern town of Kidal.
The UN called it a "revenge attack".
Chadian soldiers have twice abandoned positions in northern Mali over the last year over unpaid salaries.
Chad is a key contributor to the UN mission in Mali, which currently has 9,000 troops on the ground.
International troops have been in Mali since Islamist forces seized the north of the country four years ago.
The government of Chad has previously accused the UN of neglecting its troops in northern Mali, saying they are placed in great danger, and lack logistics and adequate food supplies.
A dozen other Chadian soldiers accused of "disobedience" have also been arrested at the same base, AFP news agency reports, quoting unnamed UN sources.
The UN peacekeeping mission in Mali has launched an inquiry after a Chadian soldier opened fire inside a UN base, killing his own commander and a doctor in the unit.