The legislative chamber invoked section 157 (1) of the constitution to send a written address to the president after it secured two-thirds majority.
The red chamber took the decison following a motion sponsored by Opeyemi Bamidele, majority leader of the senate, on Wednesday.
In July, Tinubu appointed Mainasra Kogo as new CCT chair to take over from Umar who was appointed in 2011. However, Kogo has not assumed office yet.
Section 22 of the CCT law said the president can only remove the chair or a member of the tribunal except with a written address by the house of Representatives and senate.
Umar has faced corruption allegations and even assaulted a security guard in Abuja in 2021.