He made his debut in September 1996 and he has scored 32 career tries and kicked 35 points to date.
Dempsey joins fellow Ireland internationals Gordon D'Arcy, Shane Horgan, Brian O'Driscoll in the extended panel.
Ireland back rower Sean O'Brien has also made the Leinster squad for Sunday's clash. He has been sidelined since breaking his leg against the Scarlets in February.
The Leinster team and replacements for the Edinburgh encounter will be announced on Friday afternoon.
Happy Heart Weekend is coming up on May 13 and Leinster Rugby is lending its support by organising a mobile phone collection at the Leinster v Edinburgh match on Sunday in aid of the Irish Heart Foundation.
The Irish Heart Foundation needs your old mobile phones to raise vital money to support people affected by heart disease and stroke.
LEINSTER Squad (v Edinburgh) - Backs (14): Shaun Berne, Gordon D'Arcy, Girvan Dempsey, Shane Horgan, Rob Kearney, Simon Keogh, Ian Madigan, Fergus McFadden, Isa Nacewa, Paul O'Donohoe, Brian O'Driscoll, Eoin O'Malley, Eoin Reddan, Jonathan Sexton.
Forwards (15): Leo Cullen, John Fogarty, Cian Healy, Jamie Heaslip, Nathan Hines, Stephen Keogh, Kevin McLaughlin, Sean O'Brien, Malcolm O'Kelly, Mike Ross, Rhys Ruddock, Dominic Ryan, Richardt Strauss, CJ van der Linde, Stan Wright.