The shop is located on the Upper Mall and will be there for six weeks and open seven days a week.
Fans will be able to see the key points in the club's history as well as have the opportunity to see vintage memorabilia, peruse old programmes and become involved with a series of events spread throughout February.
Karen Staniforth, Assistant General Manager at Frenchgate commented: “We have a great relationship with Doncaster Rovers and are thrilled that we will be hosting their pop-up store.
“We are always striving to offer our customers something new and the Doncaster Rovers store does just that. I am sure it will be a big hit and we are looking forward to welcoming the club to Frenchgate.
Club Doncaster marketing manager Mark Hughesman said: “Frenchgate has given us a brilliant opportunity to celebrate 140 years of Rovers with such a prominent space.
“Both fans and the community at large have an opportunity to engage with the history of their local club as well as learn more and enjoy taster sessions of the activities delivered by the Foundation.
“With events planned throughout the month within the hub, this presents a fun and engaging set of activities for young and old, fans and the wider community - everyone is welcome.”
The club was founded in 1879 by railway worker Albert Jenkins who formed the team with colleagues.