Worried about his team's form, Arthur asked each member of his squad to produce, by email or in person, three ideas about how the team could improve.
The players had five days to provide their views but the quartet failed to make their points at a team meeting.
Hoggard 'baffled' by punishments
Although all-rounder Watson, 31, has returned home, pacemen Mitchell Johnson, 31, James Pattinson, 22, and batsman Khawaja, 26, will be considered for the fourth Test.
South African Arthur, Australia's first overseas coach, told
a news conference:
''I asked the players at the end of the last game to give me an individual presentation.
"I wanted three points from each of them - technically, mentally and team - as to how we were going to get back over the next couple of games, about how we were going to get ourselves back into the series.
''I believe those four players unfortunately did not meet my requirements so those four players are not available for selection for this Test match.''
He added: "We've given an expectation that is spelt out and although this incident might seem very small in isolation, this is a line in the sand moment for us as a unit in our quest to become the best in the world.
Australia travel to England in the summer for a five-Test Ashes series that begins at Trent Bridge on 10 July and runs until late August.
Alastair Cook's team then fly down under in October to prepare for a five-Test series that starts on 21 November and ends in Sydney with the final Test on 3 January, 2014.
''This has been the toughest decision that myself, manager Gavin Dovey and captain Michael Clarke have ever had to make.
''It's a tough, tough decision, but the ramifications for that within our team structure and the message that it sends to all involved in Australian cricket is that we are pretty serious about where we want to take this team.''
Arthur's stance has drawn criticism from former Australia players.
Ex-captain Allan Border
told Fox Sports News:
"I'm surprised that's the penalty for something so mundane. It seems like it was on a schoolboy tour or something. It's an over the top reaction."
Mark Waugh added: "I've never heard anything so stupid in all my life. It's not under-sixes - this is Test cricket."
Australia now head into the third Test at Mohali on Thursday with 13 players to choose from - and that could drop to 12 if Matthew Wade fails to recover in time from an ankle injury.
The first Ashes Test begins on 10 July at Trent Bridge.
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