Armed men on Tuesday arrested ex-prime minister Modibo Sidibe and Soumaila Cisse, a former minister who led the West African Economic and Monetary Union until November last year.
Cisse suffered an unspecified injury while fleeing his home, and was later arrested at a hospital and taken by ambulance to the junta's headquarters in Kati, near Bamako, his office said.
Cisse's home was "vandalised" and a nephew and a caretaker were also injured, the office said.
Both Sidibe and Cisse were leading candidates in a presidential election set for 29 April that was derailed by the 22 March coup.
Aides to Mali's interim president Dioncounda Traore, who took office following a 6 April deal brokered by the Economic Community of West African States (ECOWAS), said he had no prior knowledge of the raid.
On Tuesday, Traore satisfied a key condition of the ECOWAS deal by naming a prime minister to head a unity government that will include the military.
The new premier, Cheick Modibo Diarra, is a noted astrophysicist who served as Microsoft's chairman for Africa and taught mechanical and aerospace engineering at Howard University in Washington DC.
Also a US citizen, he had planned to run in the aborted election this month as the candidate of the Rally for Mali's Development that he founded last year.
"We must, according to our abilities, be fully committed in order to find solutions, lasting solutions, to this problem here and to regain the totality of our country, its integrity," the 60-year-old Diarra said on public television.
But as Diarra takes charge of the interim government, he will have to contend with the junta which observers said carried out the high-profile arrests to show it has no intention of being sidelined by politicians.
"The arrest (of Cisse) clearly shows the junta's desire to not cede power to civilians," the former minister's office said in a statement sent to AFP in Dakar.
"We will hold the junta and its allies responsible for anything that happens to Soumaila Cisse," the statement added.
One of Sidibe's family members said "several armed men including two or three wearing masks" raided his home, arresting him for the third time since the coup.
Police chief Mahamadou Diagouraga, former defence minister Sadio Gassama and Hamidou Sissoko, a top aide to ousted president Amadou Toumani Toure, were among the others arrested in the overnight raids and whisked to Kati.
In a statement released late Tuesday, Colonel Moussa Sinko Coulibaly, adviser top the junta head, confirmed that "civil and military figures" had been picked up on the basis of "serious information."
Investigations into the activities of those seized were underway and legal action may be taken against them, he added, without identifying the detainees, saying how many had been arrested or saying what they were accused of.
A Malian security source said the arrests would be explained "when the time comes."
The FDR, grouping political parties and civil society groups, accused their junta of seeking to instil "a climate of terror".
A statement from European Union foreign policy chief Catherine Ashton's office demanded the "immediate release" of Sidibe and the others, calling for "urgent clarification" regarding the circumstances of their arrest.
Besides dealing with the junta, Diarra, who worked on several space exploration missions for NASA, will have to negotiate with Tuareg and Islamist rebels as well as various criminal groups who took advantage of the coup to overrun much of the country's north.
Initial contacts have been made with some of the groups since Traore's inauguration, and he has vowed "total and implacable war" if talks fail.
The low-ranking army officers who staged the putsch justified their action by denouncing the government's ineffective resistance to the Tuareg rebellion, which was rekindled in January.
The coup prompted the rebels, joined by Islamists, to capture an area roughly the size of France, including the ancient town of Timbuktu.
The main Tuareg rebel group Azawad National Liberation Movement (MNLA) then declared an independent state, drawing international condemnation.
A member of MNLA's political branch said Monday that a first official meeting between the rebels and Malian authorities had gone well and mooted the possibility of a federation.
The make-up of the new interim government was to be decided later this week.
But the length of the transition period is a key stumbling block. Under the constitution, an interim presidency should last only 40 days, but the ECOWAS-brokered deal recognised that it could take longer to organise new elections and return Mali to constitutional rule.