The figure surpasses a target of 4 million tonnes that was set by the government at the beginning of the season.
The agriculture ministry has said it was committed to buying any wheat that local farmers wished to sell until the season ends. The supply ministry has said it would probably end local procurement in mid-June.
Farmers are being paid a fixed price of 420 Egyptian pound ($47.30) per ardeb (150 kg) of wheat after Egypt abandoned plans to pay farmers global rates for their crop this year.
Egypt's wheat harvest begins in April and runs through July. Last year, the government said it procured a record 5.3 million tonnes of the grain, up from 3.7 million the year before.