Wicketkeeper Craig Kieswetter and all-rounder Samit Patel have been recalled for both squads while fast bowler Steven Finn is also a surprise selection.
Collingwood, who retired from test cricket at the start of the year, is England's most capped one-day player but has been out with a knee injury.
Kieswetter's return at the expense of Prior had been widely expected as England's test keeper has struggled to reproduce his best form in the limited-overs game.
"Paul Collingwood has been an inspirational limited-overs cricketer for England over many years and we still see a role for him in this capacity based on form and fitness," national selector Geoff Miller said in a statement.
"His omission is purely down to form over a period of time." Bowler James Anderson has retained his place after being left out during the recent World Cup.
England play a solitary Twenty20 against Sri Lanka on June 25 before embarking on a five-match one-day series starting June 28.
Stuart Broad (captain), Ian Bell, Ravi Bopara, Jade Dernbach, Steven Finn, Craig Kieswetter, Michael Lumb, Eoin Morgan, Samit Patel, Kevin Pietersen, Graeme Swann, Chris Woakes, Luke Wright England one-day squad: Alastair Cook (captain), James Anderson, Ian Bell, Ravi Bopara, Stuart Broad, Jade Dernbach, Steven Finn, Craig Kieswetter, Eoin Morgan, Samit Patel, Kevin Pietersen, Graeme Swann, Jonathan Trott, Chris Woakes
