Sellers can drop tickets at the store ahead of a show, at which point the buyers receive a text alert.
It has already launched in Fopp's Manchester store, and will roll out nationally by the end of the year.
Founder Richard Davies said the initiative was about "convenience".
"It enables people to drop off and pick up tickets in their own time and in a secure way at locations at the heart of many UK cities, and close to most venues," he said.
Davies launched Twickets in 2011, after he saw a fan offering to give away tickets to a show for free on Twitter instead of letting them go to waste.
The London-based web designer believed many other people would rather sell tickets to music, sport or theatre events at cost price, or less, to real fans, rather than cash in and sell them at a profit through secondary ticket websites like Seatwave and Viagogo.
His service began as a Twitter account, putting buyers and sellers in touch with one another. But it grew quickly, launching an app in 2013, and attracting the attention of artists like One Direction and Adele - both of whom have encouraged fans to use the service.
The site is currently selling tickets to the V Festival, and Morrissey's Manchester show, both taking place this weekend, this year for less than face value.
One Direction even sold 6,000 tickets for their On The Road Again tour directly through the site - although it is worth noting that Twicket's backers include artist management company Modest, whose clients include One Direction.
Twickets adds a 10% fee to every sale. "Drop and collect" tickets will attract a further Â£2.50 handling charge per transaction.
Specialist music retailer Fopp, which is part of the HMV Retail group, currently has nine branches across the UK.
It said the partnership with Twickets was "a great fit".
Other secondary ticketing websites, including the Ticketmaster-owned Seatwave, already offer collection points near major venues; and say that about 10% of their inventory sells for less than face value.
Follow us on Twitter @BBCNewsEnts, on Instagram at bbcnewsents, or email entertainment.news@bbc.co.uk.
Ticket site Twickets, which allows fans to sell unwanted concert tickets at face value, has set up a "drop and collect" service in Fopp record shops.