Monarch previously worked with specialist travel PR firm KTA PR, though this relationship ended in December after 12 months.
Before that, the airline worked with Mission PR.
Monarch said: "We operate in a competitive market and the time is right to appoint an agency that can help us raise our profile."
The airline hopes to have the new agency installed by March this year.
Monarch was founded in 1962 and is the oldest airline within the UK still trading under its original name. The airline is headquartered at Luton and employs about 3,000 people across the group.
In December last year, Monarch unveiled a multimedia advertising campaign that featured stories from its employees.