Georgette Ayeh, aged 39, and her five-year-old daughter from Harehills could have travelled to Heathrow.
She is described as black, of medium build, with curly blonde hair. Her daughter is black and has dark hair. It is not known what they were wearing.
Acting Detective Inspector James Entwistle, of Leeds District CID, said: "We are very concerned for Georgette's and her daughter's welfare and we urgently need to establish their whereabouts and check that they are okay.
"They have links to Leeds but we believe they may have travelled to Heathrow. We would like to hear from anyone who has seen them or who has any information that could assist in tracing them."
Anyone with information is asked to contact Leeds District CID via 101 quoting log number 553 of April 6.