On December 24, Ganesh Burman, the placement agency owner, was first detained and then arrested the same day, they said.
Two days later, police arrested the alleged woman agent, Saraswati, who had brought the maid from her employer's home after she was "physically assaulted".
Before that, Atul Kr Lohia, who had employed the victim, was arrested on December 24 following a complaint that he had allegedly physically assaulted her.
Police found that Barman used to lure women through agents from areas like West Bengal on the pretext of jobs in Delhi.
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They said the maid was suffering from tuberculosis and when her condition deteriorated, she took her to RML hospital and left, they added.
Police said the agent and the placement agency owner allegedly used to threaten to file cases against employers of the maids and extort money from them.
Burman was remanded to police custody till December 29.