Henshaw is joined in the back-three by Connacht's record try scorer Fionn Carr and Matt Healy, who touched down against the Scarlets. Former Scotland international Dan Parks has been named at out-half.
Up front, Ronan Loughney starts at loosehead prop in place of the injured Brett Wilkinson. Michael Kearney has been handed his first start of the season after coming off the bench in the last two PRO12 games. At 6ft 5in, the 22-year-old joins captain Craig Clarke in the second row.
Eoin McKeon returns to the side after missing three months due to injury. The back rower, who played 80 minutes for club side Buccaneers last weekend, starts at number 8.
CONNACHT (v Edinburgh): Robbie Henshaw; Fionn Carr, Eoin Griffin, David McSharry, Matt Healy; Dan Parks, Kieran Marmion; Ronan Loughney, Sean Henry, Nathan White, Michael Kearney, Craig Clarke (capt), Aly Muldowney, Jake Heenan, Eoin McKeon.
Replacements: Jason Harris-Wright, Denis Buckley, Rodney Ah You, Michael Swift, John Muldoon, Frank Murphy, Craig Ronaldson, Gavin Duffy.