Abbott picked up the injury during Saturday's Sydney derby at the SCG between Sydney Sixers, the team he represents, and Sydney Thunder. He impressed in that outing, picking up 2 for 28 in a high-scoring game that Sixers eventually won in the one-over eliminator.
"It is extremely unfortunate for Sean, who is very much a part of our white-ball squad plans leading into the ICC T20 World Cup and the World Cup," Trevor Hohns said in a CA statement. "D'Arcy offers the squad another spinning all-rounder option along with Ashton Agar, which, along with the four world-class fast bowlers and Adam Zampa, balances the squad out nicely.
"His proven record and ability to bat anywhere in the order will also be a great asset to the squad."
Abbott, whose only ODI appearance came in 2014, is expected to be sidelined for three to four weeks.
Short, meanwhile, has so far struck two half-centuries in three BBL innings this season for Hobart Hurricanes. He has made 120 runs overall at a strike rate of 127.65. He has played four ODIs, the last of them in November 2018, as well as 20 T20Is.
The first India v Australia ODI will be played in Mumbai on January 14, followed by matches in Rajkot (January 17) and Bengaluru (January 19).