Bradford-based Morrisons said the concession was an "individual opportunity" made possible by the refurbishment of the Idle store, but analysts believe Morrisons will roll it out across the country if it proves successful.
Peacocks said the 6,000 sq ft store in Morrisons Idle will create over 45 jobs and will offer customers "the latest fashion for ladies, men and children at great value".
Over 30 new ladies' lines will be introduced each week, including the latest nautical fashions and tribal styles, designer inspired handbags and this season's new mid-heel.
Morrisons Idle store manager Julie Lees said: "We're delighted to be opening our new concession, offering customers this season's looks at great value. With over 30 new ladies' wear lines landing in our new store each week, we're looking forward to making it easier for customers to keep on top of this season's fashion as part of their weekly shop."
Tim Bettley, Peacocks' managing director, said the deal was part of the firm's "ongoing expansion".
If successful, the deal with Peacocks could help Morrisons win more customers who are attracted to the store by a recognised high street clothing brand.
It is understood that the 6,000 sq ft space had been reserved for alcohol.
A Morrisons spokesman said the concession opportunity had been identified at the Idle store as part of its refurbishment.
Morrisons' arch rival, Leeds-based Asda, has seen sales soar at its George clothing range. Asda's highly regarded budget clothing offer is seen as a major draw for shoppers who might shop elsewhere if it didn't exist.
Morrisons' new chief executive Dalton Philips will be keeping a close eye on how the Peacocks concession performs at the Idle store.
He is keen to explore new ways to increase sales as the nation's four leading supermarkets gear up for another tough year as spending cuts and tax increases hit consumers' pockets.
Analysts believe the link-up with Peacocks is a smart move as it is a well-known high street brand which has successfully brought itself up to date by introducing new lines such as the Pearl Lowe range designed exclusively for Peacocks and modelled by daughter Daisy Lowe.
An attempt to build a new brand from scratch would have been a lot riskier.
Morrisons is expected to trial the Peacocks concept in other stores later this year if the Idle trial proves a success.
Peacocks, which dates from 1884, has 500 stores in the UK, including 70 in Yorkshire. The company floated in 1999 and was taken private by a consortium of investors in 2006.