Chaudhry, now the leader of the Fiji Labour party, refused to comment.
Bainimarama has said his interim government will pave the way for a return to democracy, but has not yet set a deadline for new elections.
Jona Senilagakali, the former interim prime minister who is a political novice and Bainimarama's doctor, was appointed health minister.
Ratu Epeli Nailatikau, a former military commander and speaker of parliament, will act as foreign minister.
Looking to China
Nailatikau said the new government would build alliances with China and other Asian nations after being shunned by Australia and other South Pacific neighbours for coming to power in a coup.
Fiji's tourist- and export-dependent economy has plummeted since a bloodless December 5 putsch and the damage was worsened by sanctions and diplomatic rebukes from Australia, New Zealand, the US, Europe and other Pacific island countries.
Nailatikau said the government would try to restore trade and diplomatic ties with its neighbours, but that it would also seek to strengthen ties with China and other Asian countries.
"We've gone north in the past on the other occasions and we will probably do the same this time," he said.
A former navy officer, a lawyer, two former senators and two failed candidates in the 2006 election were also named to top-level posts.
More appointments are expected on Tuesday.
The interim ministers were selected by Bainimarama but officially sworn in by Ratu Josefa Iloilo, the president who was ousted last month but restored to the largely ceremonial post on Thursday.
Bainimarama had earlier deposed Iloilo, dissolved cabinet, suspended parliament and banished Laisenia Qarase, the elected prime minister, to his home island 300km outside the capital, Suva.