The judge, Ahmed Refaat, set September 11 as the date for Tantawi to appear in the court, Pan-Arab news channel Al-Arabia reported.
Refaat also summoned the Army's Chief of Staff Sami Anan; Omar Suleiman, Mubarak's former intelligence chief who was also Vice President for a brief period, and Interior Minister Mansur al-Essawy.
Suleiman had disappeared from public view after mid-February when he made the televised announcement that Mubarak was surrendering power.
But in an extraordinary step, the judge stipulated that the three key men in Egypt would testify under the strictest secrecy. Not only did he order a closed session for their testimony, he also placed news organisations under strict constraints about what they could report.
The summoning of the military junta troika, the New York Times reported from Cairo, had sharpened doubts about whether the court is acting independently or cooperating with the ousted President''s former allies.
The paper said the trial had almost degenerated into a soap opera, opening with dramatic images of the former President lying on a gurney behind bars in the prisoner's dock and then descending into a confusion of questionable testimony, an apparent reference to change of testimony by a police witness.
Mubarak is being tried on charges of corruption and conspiring to order the killing of unarmed demonstrators in his final days in power.
The three witnesses including Tantawi, who is virtually de-facto President of the country, may prove crucial for the fallen President as they were within Mubarak's inner circle at that time.
Al-Arabiya said it was not clear whether the two officers, Field Marshal Tantawi and General Anan, had volunteered to testify.
Anan will give evidence on Monday and Omar Suleiman on Tuesday behind closed doors, judge Ahmed Refaat said.
Current Interior Minister Mansur al-Essawi and his predecessor Mahmud Wagdi will testify on September 14 and 15 respectively, he added.
Refaat said he had decided to hear the high-profile witnesses in camera for reasons of "national security." Lawyers acting for the families of those killed during the popular uprising that forced Mubarak out of power in February had repeatedly requested that the court hear the testimony of the five.