The Aussie batsman, who has been captaining Middlesex in County, was forced to miss a match on Sunday after being forced into isolation following a positive test result.
The 29-year-old joins the squad to fill a void left by the retirement of George Bailey at the end of last year's BBL edition.
All-rounder Glenn Maxwell, who hasn't played for Australia since last October, made the cut to the list, while Handscomb, Shaun Marsh and Nathan Coulter-Nile were ignored.
Australian cricketer Peter Handscomb has said that while it's disappointing to not be in England for the County season, there is a bigger picture at play.
Peter Hanscomb has so far made 40 appearances for Australia in all three formats of the game and is the current captain of Victoria and won three titles with them.
Peter Handscomb was called as a replacement for Shaun Marsh, who fractured his forearm after being struck in the nets last week.
Shaun Marsh has had scans on his right forearm after being struck while practising in the nets at training on Thursday, said coach Justin Langer.
Ashton Turner on Sunday smashed unbeaten 84 off 43 balls as Australia chased down a mammoth target of 359 with four wickets in hand and 13 balls to spare to level the five-match series 2-2 in Mohali.
Playing only his second ODI, Turner hit an unbeaten 84 off 43 balls with five boundaries and as many six sixes to help Australia win in only 47.5 overs.
India and Australia will look to fill the gaps when they take on each other in the five-match ODI series, starting on Saturday in Hyderabad.
Peter Handscomb was picked ahead of regular wicket-keeper Alex Carey in the first T20I against India at Visakhapatnam, giving a boost to his hopes of making Australia's World Cup squad.
Handscomb said the nearly-washed out day four of the fourth Test at the SCG has given his side a great chance to draw the match and restrict India's margin of series win to 2-1.
Tim Paine said that they just want to have a balanced team which could win the final Test.
The MCG crowd started booing Marsh once Marsh's name was announced on the public address system when he came onto bowl.
Handscomb said the conversation with Lehmann took place more than 20 minutes before he went onto the field, which he only did when another player had to use the bathroom.