Mr Badie is accused of inciting the violence in Cairo on Monday in which more than 50 people were killed.
Many Brotherhood members are already in detention and warrants are said to have been been issued for hundreds more. It comes as the interim prime minister attempts to form a government after the overthrow of President Mohammed Morsi.
The Brotherhood, to which Mr Morsi belongs, says his ousting by the military a week ago amounted to a coup.
Its supporters have since been staging large protests outside the Rabaa al-Adawiya mosque in the capital, demanding his release from detention and reinstatement.
The movement’s political wing, the Freedom and Justice Party (FJP), has said it will not accept an offer to join the cabinet being set up by interim Prime Minister Hazem al-Beblawi, a 76-year-old economist and former finance minister who was appointed on Tuesday.
The arrest warrants could scupper any attempts to persuade the Brotherhood to participate in the transitional political process.
Spokesman Gehad el-Haddad said the charges against Mr Badie, known as the General Guide, and other senior leaders, were “nothing more than an attempt by the police state to dismantle the Rabaa protest”.
“In a police state when the police force are criminals, the judiciary are traitors, and the investigators are the fabricators, what can one do?” he asked in an interview with the Reuters news agency.
A judicial source told the AFP news agency that prosecutors had issued warrants for more than 200 other Brotherhood members. They were wanted on suspicion of murder, incitement to violence, carrying unlicensed weapons and disrupting public order, the source added.
There were conflicting reports about what happened on Monday, with the interim authorities being accused of a cover-up. The Brotherhood maintains that soldiers carried out a massacre of peaceful demonstrators, who had been taking part in dawn prayers outside the Presidential Guard barracks, where many believe Mr Morsi is being detained.
But the police and the military say they acted in self-defence, and had opened fire only after being attacked by armed assailants.
More than 50 Brotherhood supporters were killed, as well as a soldier and two policemen.
The previous Friday, Mr Badie had appeared at a rally outside the mosque, telling the crowd: “We shall stay in the squares until we bring President Morsi back to power.”
He said their protests would remain peaceful and called on the army not to “direct your arms against us”.
The BBC’s Jim Muir, in Cairo, says the protest now covers several square kilometres of the capital, and to clear it out forcibly would almost certainly involve further bloodshed.
There is a feeling among the protesters that they have returned to the situation they were in under former President Hosni Mubarak, when the movement was banned and its members hunted down, our correspondent adds.
The timetable for new elections, announced by interim President Adly Mansour on Monday evening, laid out plans to set up a panel to amend the suspended constitution within 15 days.
The changes would then be put to a referendum – to be organised within four months – which would pave the way for parliamentary elections, possibly in early 2014. Once the new parliament convenes, elections would be called to appoint a new president.
A spokesman for Mr Mansour said posts in the cabinet would be offered to the Freedom and Justice Party, which won Egypt’s first free parliamentary elections.
But Mohamed Kamal, a senior official in the FJP, told the BBC: “We will never take part in any cabinet as long as Morsi is not back as a president.”
The party’s deputy chairman, Essam al-Erian, earlier called the election timetable “a constitutional decree by a man appointed by putschists”.
The main liberal coalition, the National Salvation Front (NSF) has expressed its reservations about the decree, saying it was not consulted.