Pardeep Kaur, from south-west London, was reported missing by a relative earlier this week, having failed to turn up for work.
Metropolitan Police murder detectives said the disappearance was out of character and they were "extremely concerned" for her safety.
Met Police Detective Chief Inspector Mark Lawson said: "Our enquiries have led us to make these two arrests but until we have evidence to the contrary, we continue to treat Mrs Kaur as a missing person.
"We are extremely concerned for her welfare as her disappearance is completely out of character. If you think you have seen Pardeep since her disappearance on Sunday, or have any information about her whereabouts, please get in touch with police as soon as possible."
Two men, aged 30 and 31, were arrested over her disappearance.
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