Nicola Goodhine, 37, was last seen on Toynbee Road, Eastleigh, at 12.55pm on Thursday, May 1.
Police said they are “extremely concerned” for her welfare.
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Nicola is described as white, approximately 5ft 8ins tall, of skinny build, with short brown hair.
She was last seen wearing a white or blue headscarf, grey cardigan, denim shorts, black Dr Martens boots, and carrying a black square bag.
Anyone with information about her whereabouts is urged to call 999, quoting incident number 44250189142.