It will be Sheehan's first start for Ireland since suffering a serious knee injury against South Africa in Pretoria eight months ago.
His inclusion is among seven changes made by coach Simon Easterby from the side that beat Scotland 32-18 at Murrayfield two weeks ago.
Easterby has handed opportunities to players who have been knocking on the door for selection like fullback Jamie Osborne, who replaces Hugo Keenan.
In the front row, Finaly Bealham is rested to allow Thomas Clarkson a first Test start after four substitute appearances while uncapped Jack Boyle gets a berth on the bench.
The coach also brings back Gary Ringrose to partner Robbie Henshaw at centre while Australian Mack Hansen returns to the right wing after a hamstring injury meant he could not face Scotland.
Joe McCarthy suffered a head knock in a non-contact drill days before Ireland's first match of the competition against England but he returns at lock in place of James Ryan.
Regular captain Doris misses out due to a knee injury after playing in each of Ireland's last 41 tests and is replaced at number eight by Jack Conan.
New skipper Sheehan, 26, has come off the bench in their opening two wins against England and Scotland. He replaces Kelleher, who has a neck injury.
"We have made a few changes to the squad this week, some of which were enforced, and we're confident that the 23 we have selected are primed and ready to go," said Easterby in a statement.
"Dan Sheehan's selection as captain is recognition of his high standing within the squad, both on and off the pitch," he added.
Team: 15-Jamie Osborne, 14-Mack Hansen, 13-Garry Ringrose, 12-Robbie Henshaw, 11-James Lowe, 10-Sam Prendergast, 9-Jamison Gibson-Park, 8-Jack Conan, 7-Josh van der Flier, 6-Peter O'Mahony, 5-Tadhg Beirne, 4-Joe McCarthy, 3-Thomas Clarkson, 2- Dan Sheehan (captain), 1-Andrew Porter
Replacements: 16-Gus McCarthy, 17-Jack Boyle, 18-Finlay Bealham, 19-James Ryan, 20-Cian Prendergast, 21-Conor Murray, 22-Jack Crowley, 23-Bundee Aki.
