The commission published a list of 50 people suspected of corruption on February 18, including politicians, former bureaucrats, trade union leaders and businessmen, and had asked them to submit an account of their wealth by Sunday.
It warned that those who did not meet the deadline could have their assets and property seized.
Abbas was a minister under former prime minister Khaleda Zia during her 2001-2006 term, while Hossain sat in the cabinet of Zia's arch rival, Sheikh Hasina, during her 1996-2001 stint as prime minister.
Zia's five-year term expired in October, and she handed power to a caretaker government to oversee elections in line with the constitution. But Hasina accused the interim government and the election commission of favouring Zia and her party, and led months of often violent protests to call for electoral reforms.
State of emergency
Iajuddin Ahmed, Bangladesh's president, declared a state of emergency on January 11 and security officials have been given sweeping powers to make arrests without a warrant.
Ahmed also cancelled elections, originally slated for January 22, and appointed Fakhruddin Ahmed, a respected economist and former World Bank official, as a new interim leader.
Fakhruddin Ahmed last month vowed to flush out corrupt political elements before holding elections, although no new date for the polls has been set.
Earlier, security officials backed by troops arrested about 30 people, including former ministers, legislators, and businessmen accused of graft, according to police headquarters.
The detained politicians mainly belong to either Zia's Bangladesh Nationalist Party (BNP) or Hasina's Awami League party.
Mohammad Giasuddin, a former BNP legislator, surrendered to a court in Narayanganj district on Sunday, the United News of Bangladesh said.
Hafiz Ibrahim, another BNP legislator, was arrested as he submitted his wealth statement to the commission, as was a former top bureaucrat of the country's power ministry.