The child, Daniella Topple, was taken by her mother Ogonna Topple, 29, after an access visit on Saturday afternoon in the Bruntsfield area of Edinburgh.
Police fear that the Nigerian national may attempt to take the four-year-old out of the country after she failed to return Daniella to her father.
She was wearing a dark-brown corduroy hat and a leather necklace with a bullet-shaped pendant. The mother had been staying in a guesthouse in the city, but cleared out her belongings on the day she and her daughter disappeared.
A police spokesman said: "We are anxious to trace Daniella and her mother and would appeal to anyone who may have seen them in the Bruntsfield area or has any knowledge of their current whereabouts to contact the police.
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