The outgoing left-wing leader and the centre-right president-elect disagree over where the ceremony should be held.
Ms Fernandez bid farewell to a large crowd of her supporters in an emotional speech on Wednesday.
She urged people to take to the streets if they felt betrayed by the new centre-right government.
Mr Macri will take his oath of office before legislators in Congress at noon local time (15:00 GMT).
Following his inaugural speech, he will then travel to the presidential palace where he will receive the presidential sash and baton.
Ms Fernandez had insisted that the handover should also take place in Congress, where her party holds a majority of seats.
She argued that both she and her husband and predecessor in office, Nestor Kirchner, had received the symbols of power in Congress and it had therefore become a tradition to be followed.
Mr Macri argued that according to presidential protocol, the handover should be held in the presidential palace, as it did before 2003.
Local media reported that Mr Macri’s decision was probably driven not just by tradition but also by a concern that followers of Ms Fernandez could disrupt the ceremony in Congress.
Aides to Mr Macri said they feared her party could fill the gallery with her hardcore supporters.
Annoyed by Mr Macri’s insistence, Ms Fernandez announced she would skip both ceremonies altogether.
Mr Macri’s party in turn sought a court injunction affirming that Ms Fernandez’s term ended at midnight on Wednesday to settle the matter.
As a result, power was temporarily transferred to Senate Speaker Federico Pinedo, who is acting as head of state for 12 hours until Mr Macri’s inauguration.