Paige Holland, 23, who gardaí say is also known as Abbie Goodier or Paige Goodier, left her home at Westview, Cloonfad in Co Roscommon, on January 15 with her daughter Nevaeh Goodier/Tighe.
Nevaeh was only born two days earlier on January 13.
Gardaí believe Paige and Nevaeh are travelling with Paige’s boyfriend Aaron Tighe, 22.
According to gardaí, he is also known as Aaron Chadwick or Ian Smith.
A Garda spokesman said both Paige and Aaron have strong English accents.
Paige Holland is described as 5ft 6in, of medium build with blonde, shoulder-length hair.
Gardaí said it is not known what Paige was wearing when she was last seen.
Aaron Chadwick is described as 5ft 6in, of medium build, with short brown/fair hair.
Gardaí said they do not know what form of transport the three are using and say they may be travelling on public transport.
“Gardaí are requesting Paige to make contact with Castlerea Garda Station as soon as possible,” a spokesman said.
“Gardaí are concerned for the welfare of Paige and her daughter and anyone with information is asked to contact Castlerea Garda Station on 094 9621630, the Garda confidential line, 1800 666111 or any Garda Station.”