Isa Nacewa, who scored all of Leinster's points against Benetton Treviso, will don the number 10 jersey in his place.
The 21-year-old Ian Madigan comes onto the replacements bench.
Sexton has yet to make his seasonal bow for Leinster, which, fitness permitting, should come in next week's much-anticipated clash with Munster at the Aviva Stadium.
LEINSTER (v Edinburgh): Rob Kearney; Shane Horgan, Brian O'Driscoll, Gordon D'Arcy, Luke Fitzgerald; Isa Nacewa, Eoin Reddan; Heinke van der Merwe, Richardt Strauss, Mike Ross, Ed O'Donoghue, Devin Toner, Dominic Ryan, Shane Jennings (capt), Stephen Keogh.
Replacements: Jason Harris-Wright, Cian Healy, Simon Shawe, Mariano Galarza, Jamie Heaslip, Isaac Boss, Ian Madigan, Eoin O'Malley.