The selection panel reasoned that pitches in Perth, Melbourne and Sydney would assist quick bowlers so there was no need for a specialist spinner at least for the first three ODIs of the five-match series.
The selectors named uncapped left-arm paceman Joel Paris, who has the ability to swing the ball well, and Scott Boland while Kane Richardson also returned to the side having last played for Australia against South Africa in Canberra in 2014.
There was no place in the squad for Watson, Joe Burns and James Pattinson.
Also Read
Chairman of selectors Rod Marsh said both Scott and Paris deserved to be in the squad.
"Scott has continued to impress the selection panel, having bowled very well for his state Victoria this year. He certainly deserves this chance at the top level,"
"Joel is an exciting young left-arm bowler who swings the ball well.
He has had very good figures in short-form cricket and we really want him to make the most of this opportunity."
Selector Trevor Hohns said Lyon will be considered for future matches and in his absence Glenn Maxwell will provide the spin option.
"Nathan is not far out of the picture for one-day cricket, and of course with the (World) T20 coming up it's probably ideal for him to go back and play some of those games," Hohns said.
"We're playing the first few games in Brisbane and Perth where normally you play with your faster bowlers. Glenn Maxwell has done a pretty good job in the spinning role when we're only playing that one type of spinner-cum-all-rounder, plus the quicks."
India will play five ODIs against India starting in Perth (January 12) and followed by matches in Brisbane (January 15), Melbourne (January 17), Canberra (January 20) and Sydney (January 23).
The ODI series will be followed by a three-match Twenty20 series.
The tour opener in Perth will be first match between India and Australia after the World Cup semifinal.
Australia Squad: Steve Smith (C), David Warner, George Bailey, Scott Boland, Josh Hazlewood, James Faulkner, Aaron Finch, Mitchell Marsh, Shaun Marsh, Glenn Maxwell, Kane Richardson, Joel Paris and Matthew Wade.