The woman and two children had been missing from South Gloucestershire since 17 February.
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A 50-year-old man has been arrested in Dundee in connection with the disappearance of a woman and two children.
Avon and Somerset Police issued an appeal last week to trace 25-year-old Bennylyn Burke and two children from South Gloucestershire.
Officers investigating the disappearance went to a house in Troon Avenue, Dundee, on Friday afternoon.
Police Scotland said inquiries were ongoing.
Det Supt Graeme Mackie, from the force’s major investigation team, said: “Officers in Dundee attended a property on Troon Avenue around 15:20 on Friday, 5 March, 2021, as part of an inquiry into a missing 25-year-old woman, Bennylyn Burke, and two children from South Gloucestershire.
“As a result, a 50-year-old man has been arrested in connection with this and inquiries are ongoing. Bennylyn’s next-of-kin have been made aware and are being supported by colleagues in Avon and Somerset Police.
“There will be an increased police presence in the area over the coming days and we thank the local community for their cooperation at this time.”
Det Supt Mackie asked anyone with information to speak to local officers or to call Police Scotland via 101.
Ms Burke and the two children were reported missing on 1 March. Avon and Somerset Police put out an appeal for information two days later.
The force said the 25-year-old was last seen at her South Gloucestershire home on 17 February.
A large police presence remains in Troon Avenue, which is near Downfield in the north of Dundee, with dozens of police and forensic officers at the scene.
Police Scotland has closed off the street with a cordon around the house.
A blue tent has also been erected in the front garden to cover a waste skip and yellow polythene has been used to cover windows at the back of the property.
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