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The order is legally binding, said Nizami, who is acting as a spokesman for the government.
The government must act within 24 hours of the high court decision or face contempt of court charges. It appears ready to comply with the order.
This means Musharraf could be placed under house arrest at his villa as soon as Thursday evening.
Local TV stations earlier showed police entering his villa compound, where Musharraf went after being quickly ushered from the court by his private security detail.
The arrest order was made at the same time as the court rejected Musharraf's request for a bail extension in a case he is facing over the detention of judges in 2007.
The ruling set the stage for his arrest and has further undermined his political ambitions.
Musharraf's office called the Islamabad court's decision "unwarranted judicial activism" that was "seemingly motivated by personal vendettas," and said it would appeal against it at the Supreme Court.
But Ibrahim Satti, one of Musharraf's attorneys, told local TV reporters that they had arrived at the court too late in the day and that the Supreme Court refused to accept the appeal.
Satti said Musharraf's legal team would seek to file the appeal Friday instead, local TV stations reported.
Meanwhile, the Islamabad High Court issued a ruling calling the inspector general of Islamabad police to court Friday to explain why his officers did not arrest Musharraf in court Thursday as instructed.
The high court ruling asks the inspector what precise steps police took to arrest Musharraf.
The ruling also says that when Musharraf allegedly ordered the house arrest of senior judges in 2007, it was an "act of terrorism" to prevent the judges from doing their job.
Return from exile
Musharraf resigned as president of the South Asian nation five years ago and went into exile in London and Dubai. He returned to Pakistan under heavy security to contest three court cases against him and run in upcoming elections.
But so far, his return does not seem to be going according to plan.
This week, Pakistani election officials barred Musharraf from running for a seat in parliament, a decision his lawyer has said he will challenge in the Supreme Court.
That decision appears to have emboldened members of the judiciary, many of whom have bitter memories of their treatment by Musharraf during his time in power.
The rejection of bail Thursday came in a case in which Musharraf faces accusations that he illegally imposed house arrest on senior judges during a period of emergency rule he imposed six years ago.
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