The couple have been held in police custody since Thursday on suspicion of withdrawing 110,643 ringgit (1.1 million baht) from the accounts of two Malaysian and two Chinese passengers on the doomed flight, said Zainuddin Ahmad, a district police chief in Kuala Lumpur.
Police are also looking for a Pakistani man who is believed to have received part of the money in his account through an online transfer, he added.
"We believe he is still in the country. But as to the full particulars of the case. It's all still under investigation," Zainuddin told AFP.
Zainuddin declined to name the bank, where the woman in custody reportedly worked at for the last 10 years.
The Star daily reported that the four bank accounts were with HSBC and quoted HSBC Bank Malaysia Bhd saying in a statement that it had referred the matter to the police, declining further comment.
HSBC executives could not immediately be reached.
The Malaysia Airlines plane lost contact en route from Kuala Lumpur to Beijing on March 8 with 239 people aboard and mysteriously disappeared.
The Boeing 777 is believed to have veered off course and have crashed in the southern Indian Ocean but no sign of wreckage has been found thus far.