Egyptian President Abdul Fattah al-Sisi has authorised the military to protect state facilities after jihadists killed more than 30 soldiers last week.
A spokesman said the new law gives the army the right to secure sites like power plants, main roads and bridges.
But critics say it allows the army to return to the streets and bring back military trials for civilians.
President Sisi declared a three-month state of emergency after the bomb attack in Sinai on Friday.
The new decree allows state infrastructure to be defined as "military facilities" for two years, permitting the army to work with police to secure such sites.
It also gives the military the right to try people it suspects of launching attacks on those sites.
Activists say the law is too broadly defined and could also cover universities, where police have been unable to stop student protests.
Putting an end to military trials was one of the main aims of the 2011 uprising that ousted the former president, Hosni Mubarak.
Presidential spokesman Alaa Youssef insisted the decree was aimed at tackling terrorism, not protesters, and told the BBC it was a limited, proportional response to recent attacks by militants.
The law was introduced after President Sisi promised a tough response to what he called an "existential threat" to Egypt posed by Islamist militants.
In light of the perceived threat, the editors of 17 newspapers in Egypt have decided to refrain from publishing criticism of the army or the state, the BBC's Orla Guerin in Cairo reports.
Human rights groups say it is another sign that the room for dissent in Egypt is shrinking even further, our correspondent adds.
Meanwhile, an Egyptian judge ordered 21 activists to be arrested on Monday at the start of their retrial for breaking protest laws during the military's overthrow of President Mohamed Morsi in 2013.
The activists, who had been released on bail last month, chanted "down with military rule" after the judge read out his decision in court.
The court also issued arrest warrants for four of the defendants who did not show up.
The group, which includes leading campaigner Alaa Abdel Fattah, were sentenced to 15 years in prison in absentia last June for violating a 2013 law curbing the right to public protests.
They were later arrested and tried again in person on the same charges but that trial collapsed last month when the presiding judge stepped down.
On Sunday, Mr Abdel Fattah's younger sister Sanaa, a 20-year-old student, was jailed for three years along with 23 other young activists for breaking protest laws.
Outside the courtroom on Monday, Mr Abdel Fattah said the rulings against activists like his sister were a deliberate attempt by the government to imprison and silence their critics.
The judge set the next hearing for Mr Abdel Fattah and the 20 other activists for 11 November.