Police are trying to trace Barbara Bogdan, 20, originally from Hungary, and her 15-month-old boy Kevin.
They were last seen in Dewsbury on the morning of January 25, then in Wakefield later that day when they took the 12.42pm free bus from Pinderfields Hospital into the city.
Inspector Dorian James said: “We are urging anyone who knows Barbara Bogdan and her son who can help us to find her to please get in contact.
“She is not in any trouble with the police, but we just want to speak to her to make sure her and her son are okay.
“We understand she’s had links to the Dewsbury Moor and Batley areas since coming to the UK and believe that she is still in the country.”
Anyone with information is asked to call West Yorkshire Police on 101, quoting log 1216 of January 26.