The National Education, Health and Allied Workers Union's (Nehawu) secretary in the province, Sizwe Motha, welcomed the MTPA board's action. The horns disappeared from a safe on Sunday.
The MTPA and the Mpumalanga department of economic development, tourism, and environmental affairs could not immediately be reached for comment.
AFP reported the horns could be worth around R170m.
"The CEO [Jacques Modipane] bears the ultimate responsibility and accountability on the management of the institution," Motha said.
DA provincial leader Anthony Benadie said the party was informed that acting MTPA board chair Clarah Ndlovu removed Modipane from his post on Thursday "in what appears to be a knee-jerk response to the theft of rhino horn".
"Modipane has been trying to instil good, clean... governance in the agency, and his [alleged] sacking has caused MTPA staff to go on strike this morning, demanding his reinstatement," Benadie said.
He called on Economic Development MEC Yvonne Phosa to disband the MTPA.