Veteran lock O'Kelly may require surgery on his groin problem while Easterby, O'Connor and Reddan are also missing through injury from an otherwise full-strength squad.
Ireland head coach Eddie O'Sullivan said: "I would have preferred to be dealing from a full deck for the tour, but the absences leave the door open for the players coming into the squad."
Easterby has not played since being knocked out and swallowing his tongue in the Powergen Cup final against Wasps, a match which also saw O'Connor ruled out for the season with spinal concussion.
Reddan, who supplied cover for first-choice scrum-half Peter Stringer from the bench throughout the RBS 6 Nations Championship, has been suffering from a groin injury.
O'Sullivan added: "Both Malcolm and Simon are world-class lineout operators and the tour also represented a chance for Johnny and Eoin to stake their claims for a starting berth, so they will all be missed."
Uncapped Isaac Boss takes Reddan's place and is joined in the 30-strong squad by Ulster prop Bryan Young, the only other member of the party yet to make an international appearance.
In the backs, Harlequins centre Gavin Duffy and Wasps fly-half Jeremy Staunton have been restored to the senior group after winning the last of their caps on the 2005 summer tour of Japan.
Leinster winger Denis Hickie is also included after missing the entire Six Nations, reward for his recent form in the European Cup.
Munster skipper Anthony Foley, preparing for Saturday's European Cup final against Biarritz, features as one of six back rows in an experienced squad led by Brian O'Driscoll.
Keith Gleeson, who won his last cap against Italy in 2004, will compete for the openside duties, while Leicester lock Leo Cullen replaces the injured O'Kelly.
One back row slot remains open, with O'Sullivan giving Alan Quinlan of Munster as much time as possible to prove his fitness for the tour.
O'Sullivan said: "Any tour to the southern hemisphere is tough and with two tests in New Zealand and one in Australia, this will be no exception.
"As proved by the Lions tour last year, the intensity of the game in the southern hemisphere is incredibly high and something we will have to prepare ourselves for.
"Coupled with the fact that we will be playing two of the top teams in the world, the tour will be a huge challenge."
Ireland face New Zealand on June 10 and 17 and then complete the tour with a Test against Australia seven days later.
Ireland squad for summer tour to New Zealand and Australia:
Backs: I Boss (Ulster), T Bowe (Ulster), G D'Arcy (Leinster), G Dempsey (Leinster), G Duffy (Harlequins), D Hickie (Leinster), S Horgan (Leinster), J Kelly (Munster), G Murphy (Leicester), B O'Driscoll (Leinster, captain), R O'Gara (Munster), J Staunton (Wasps), P Stringer (Munster), A Trimble (Ulster).
Forwards*: N Best (Ulster), R Best (Ulster), S Best (Ulster), L Cullen (Leicester), J Flannery (Munster), A Foley (Munster), K Gleeson (Leinster), J Hayes (Munster), M Horan (Munster), D Leamy (Munster), D O'Callaghan (Munster), P O'Connell (Munster), M O'Driscoll (Munster), D Wallace (Munster), B Young (Ulster).
*One forward still to be added to squad.