The testimony of General Sami Annan, the Chief of Staff of the Egyptian Armed Forces, has also been delayed to September 25. Annan had been due to give evidence today.
Tantāwī faced a last minute difficulty which made him unavailable to testify as scheduled yesterday, MENA and AFP said.
He is one of the highest profile witnesses called to testify at Mubārak's trial, which has grabbed widespread regional attention.
Trial judge Ahmad Rifat, during a September 7 hearing, ordered that the two senior military officials testify behind closed doors for reasons of "national security."
Earlier, television footage of the first two sessions of the trial which opened on August 3 had shown the ailing 83-year-old Mubārak, who faces charges of involvement in the killings of protesters and corruption, lying on a stretcher and in a cage in the courtroom.
The charges against Mubārak, who has pleaded not guilty, follows months of protests demanding justice for the roughly 850 people killed during the revolt which ended his regime.
The trial is being held in the Police Academy once named after Mubārak, in New Cairo, on the eastern outskirts of the capital.