Cullen is the only change in the 14-player Australian squad that lost this month's One-day series 3-2 to South Africa.
South Africa scored a world record 438 for nine to overhaul Australia's 434 for four and win the fifth match of the series in Johannesburg on March 13.
Lewis was hammered for 113 runs off his 10 overs, becoming the first player to concede 100 runs in a One-day international.
Selectors also named an unchanged 14-man Test squad for the two Test matches against Bangladesh that precede the three ODIs.
"We have brought Daniel Cullen into the One-day squad to give him an opportunity to perform at the next level," chairman of selectors Trevor Hohns said in a statement Thursday.
"It will be a good test for Daniel and we think it is the right time to give him some experience and a chance to be a part of the Australian team environment.
"Michael can count himself a little unlucky, but the opportunities are still there for him to present himself for future selection.
"We felt it was necessary to include an extra spinner in the squad to complement the four fast bowlers in best dealing with the conditions we expect in Bangladesh."
Hohns said selectors had seen no reason to make changes to the Test team following their 2-0 series win over South Africans with a Test to play.
"With the players in the current squad we feel we are well covered for the conditions that may prevail in Bangladesh," he said.
Test squad: Ricky Ponting (captain), Adam Gilchrist (vice-captain), Stuart Clark, Michael Clarke, Matthew Hayden, Michael Hussey, Michael Kasprowicz, Justin Langer, Brett Lee, Stuart MacGill, Damien Martyn, Andrew Symonds, Shaun Tait, Shane Warne.
ODI squad: Ricky Ponting (captain), Adam Gilchrist (vice-captain), Nathan Bracken, Stuart Clark, Michael Clarke, Daniel Cullen, Brad Hogg, Michael Hussey, Mitchell Johnson, Simon Katich, Brett Lee, Damien Martyn, Shane Watson, Andrew Symonds.