A motion of no confidence in President Jacob Zuma will be debated on 22 February.
National Assembly Speaker Baleka Mbete has heeded to the EFF's request but not on the day it had requested.
The EFF had wanted the debate to be held on Thursday, when Zuma is due to deliver the State of the Nation Address (Sona).
The Democratic Alliance (DA), meanwhile, has called for the address to be postponed, but Mbete says this is not within her powers to change.
The motion of no confidence will now take place on the day after the national budget is tabled by the Finance Minister.
Parliamentary spokesperson Moloto Mothapo: "With regard to the EFF request, the Speaker has indicated that she has consulted with everyone that needs to be consulted, which includes the leader of government business, as well as the leader of the majority party and she has also taken into consideration the programme of the House, which includes the State of the Nation Address, which is scheduled for 8 February."