The Aussies welcome back in-form captain Michael Clarke, who was rested from the first two matches of the series after an outstanding Test series performance against the Lankans.
Wicketkeeper Matthew Wade also returns to the Aussie squad, along with aggressive big-hitter David Warner.
Batsmen Usman Khawaja and Aaron Finch were dropped after making their day-night debuts for Australia at the MCG last Friday.
National chairman of selectors John Inverarity said Henriques would be perfectly suited to the Gabba pitch, where the Aussies face Sri Lanka in the third ODI.
The series is tied at 1-all, after Australia romped to a 107-run win in the first clash on Friday, before Sri Lanka snatched an eight-wicket win in Adelaide on Sunday night.
The Australian squad for the third and fourth matches is:
Michael Clarke (Capt)
Henriques, 25, has made two ODI appearances for Australia, but they were way back in 2009 against India.
Inverarity said Henriques' chance was as a genuine all-rounder.
“Moises Henriques also comes into the squad as a genuine all-rounder whose bowling will be suited to conditions often found at the Gabba," the chairman of selectors said on Monday.
“Moises is a young man who has shown promise for some years with both the bat and the ball.
"This will be an opportunity for him to impress as we look for a good seam bowling all-rounder.”
Veteran 'keeper Brad Haddin is also out of the squad after picking up a minor hamstring strain.
Pacemen Mitchell Johnson and Mitchell Starc were given the green light to play, forcing big Queenslander Ben Cutting and South Australian Kane Richardson out of the squad.
Finch, who scored 16 on debut in Melbourne and then four in a poor Aussie performance in South Australia, was dropped from the side to make way for returning stars.
But, Inverarity insists Finch, 26, was not hard-done-by and would be given another chance to prove himself on the international stage.
"Three or four days ago, he was a very good player worthy of contention and he still is," Inverarity said.
"I think we are likely to see him back in the T20s, he's very good and an exciting player.
"We rested David Warner, Michael Clarke and Matthew Wade, with a clear intention of bringing them back, so I don't think Aaron really expected to be retained after that."
Finch will be available for his Melbourne Renegades' Big Bash semi-final clash with Brisbane Heat on Tuesday night.