Two-test Doherty, another casualty of that series, will be expected to provide support for fellow spinner Nathan Lyon in India, where Australia have not won a test since 2004.
The 24-year-old Maxwell and Henriques, 25, would provide flexibility for the team, according to selector John Inverarity.
"The squad includes a spin bowling all-rounder in Maxwell and a medium-fast all-rounder in Henriques," Inverarity said in a media release.
"In aiming for more depth in a bowling attack, the squad would allow for three pace bowlers, a leading spinner and Maxwell or two pace bowlers, the two spinners and Henriques. These are two of the options.
"Xavier Doherty also returns to the test squad. We certainly feel he is much improved in the longer format of the game since he made his test debut in 2010-11 against England."
Opening batsman David Warner has been named despite breaking a thumb during practice this week, and Inverarity said he was confident the hard-hitting 26-year-old would recover in time for the first test which starts Feb. 22 in Chennai.
A year after being dropped following Australia's shock loss to New Zealand in Hobart, Pakistan-born batsman Usman Khawaja has a chance to add to his six tests, and has been named along with Phillip Hughes, the de facto replacement for retired former captain Ricky Ponting.
James Pattinson has been named in a five-man pace battery after missing most of the Australian summer with a rib injury, with Jackson Bird rewarded a place after taking 11 wickets in his first two tests against Sri Lanka.
The 26-year-old Bird will battle for selection with left-armers Mitchell Johnson and Mitchell Starc.
The squad will be effectively split into two, with one group to head to India earlier for warm-up matches and the second to stay in Australia for one-day games against West Indies.
Selectors will name the advance party on Saturday.
The teams play the second test in Hyderabad from March 2, with the third in Mohali (March 14) and the final match in Delhi (March 22).
The squad: Michael Clarke (captain), Shane Watson, David Warner, Ed Cowan, Phillip Hughes, Matthew Wade, Nathan Lyon, Mitchell Starc, Mitchell Johnson, Jackson Bird, Xavier Doherty, Moises Henriques, Usman Khawaja, Glenn Maxwell, James Pattinson, Steve Smith, Peter Siddle