The Luton-based airline has complained about eDreams adding service charges to Monarch flights at the end of the booking process, as well as charging for text message updates and using higher fares for children.
Monarch has now set up a blog for consumers to highlight the extra fees it says eDreams are charging holidaymakers.
The CAA has already launched an investigation into the website and pricing practices of eDreams and its sister online brand Opodo.
Monarch’s head of digital and online Ian Chambers said: “We are challenging websites like eDreams to stop them using our branding and mis-selling our flights.
“We do not have a commercial relationship with the company and do not condone their pricing policy.
“There are many reputable travel agents, who work on behalf of the customer, both on the high street and online with whom we work closely and would recommend.
“We remain committed to supporting our trade partners to ensure customers are getting the best price and service.”
Fellow airline Ryanair has been one of the biggest fighters against screen scraping in the last few years.
The carrier launched legal action in the Irish high court in December 2015 against both eDreams and Google “to stop them misleading consumers by advertising non-existent Ryanair fares via the eDreams website and Google search adverts”.