BBC correspondent Paul Wood says the detention of Mr Markovic will add to the momentum for an arrest and prosecution of Mr Milosevic.
Mr Markovic, who headed the secret police from 1998 until January 2001, has been accused by various human rights groups and Milosevic opponents of being behind a series of political killings.
Reacting to the arrest, Mr Draskovic told Serbian TV: "I hope it will not stop at this - that it will soon involve people who gave the orders."
BBC correspondent Paul Wood says the detention of Mr Markovic will add to the momentum for an arrest and prosecution of Mr Milosevic.
Earlier in the week, Serbian Prime Minister Zoran Djindjic said Mr Milosevic would soon be behind bars.
Serbian Justice Minister Vladan Batic said after the arrest: "We are entering a decisive battle against crime and in that battle no one will be untouchable."
Tribunal interest
Serbian reformers and Western diplomats said Mr Markovic could reveal much of what went on behind the scenes in the old regime, making him a potential key witness in investigations into Mr Milosevic and his influential wife Mira.
"Nobody can give better evidence against Milosevic if he starts to talk," said one Western diplomat in Belgrade. "Why should he keep silent?"
Mr Markovic, unlike Mr Milosevic, has not been publicly indicted by the UN war crimes tribunal in The Hague but a spokeswoman said the chief prosecutor would want to hear evidence from him.
"Clearly, given the sort of figure that he is, we will need to be in contact with him and interview him," spokeswoman Florence Hartmann told Reuters.
Markovic denial
"We will have to be in touch with Belgrade."
Serbian media said three other people were arrested along with Mr Markovic, including former Belgrade police chief Branko Djuric.
Mr Markovic resigned from his post on 25 January, the day that Mr Djindjic and his reformist cabinet took office.
He had been resisting calls to resign for several months, denying that his department was involved in politically motivated crimes.
But the Belgrade-based Humanitarian Law Centre (HLC) says it has documentary evidence that Mr Markovic was behind the killing last year of newspaper editor Slavko Curuvija, a harsh critic of the former president.