Since the country moved from alert level five to four on 1 May, a more rapid than expected restart of economic activity resulted in a dramatic increase in diesel demand, Sapia said.
Unplanned refinery shutdowns were a contributing factor to the shortage, it said.
All four of the country's oil refineries were shut in response to lower demand when the lockdown period started on 27 March. Demand for petroleum products fell by 60pc during the period.
Sasol's Secunda 160,000 b/d coal-to-liquids refinery is operating at around 25pc below its normal daily production rate.
State-owned PetroSA's 50,000 b/d gas-to-liquids plant at Mossel Bay halted production temporarily because of product contamination and pipeline failures, according to opposition party the Democratic Alliance.
Diesel rationing is being implemented to manage demand and preserve stock, Sapia said. But the shortage is expected to last only until the end of May as both Durban refineries have started to ramp up, it added.
Engen restarted its 105,000 b/d Durban refinery on 15 May, while the BP-Shell Sapref joint venture 180,000 b/d refinery in Durban started ramping up on 18 May.
Both refineries started around two weeks earlier than scheduled after maintenance work on the single buoy mooring (SBM) facility that handles crude tanker deliveries into the Port of Durban's oil terminal was completed early. The maintenance work was planned to last for the whole of May.
More economic sectors including mining will start operating at full capacity from 1 June when the lockdown alert level is eased further to level three.
South Africa consumed 12.5mn litres of diesel in 2018, the latest year for which Sapia figures are available.
