Both players were able to walk approximately 300 metres to a nearby clinic and showed no obvious signs of limping, News.Az reports, citing Australian media.
Cricket Australia and Cricket NSW have not confirmed the specifics of the injuries as of Wednesday.
Any injury to Hazlewood would be particularly worrying, with the first Test against England in Perth just nine days away. Australia is already without captain Pat Cummins for the series opener, with Scott Boland expected to take his place in the playing XI.
The hosts have not entered a Test match without at least some combination of Cummins, Hazlewood and Mitchell Starc in the side since December 2022.
Hazlewood has battled a number of injuries through that time, including missing three Tests last summer with a side strain.
If Hazlewood was also ruled out, Brendan Doggett would likely be called in to debut.
Doggett has taken two five-wicket hauls since returning from a hamstring injury for South Australia, and is one of the form bowlers in the country.
The South Australian was initially part of Australia's squad for West Indies and would have been a chance to debut there before suffering a side strain.
Abbott is the other back-up paceman in the Test squad. He took three wickets in six balls on Wednesday before leaving the SCG to be assessed.
The injury scares could also place more importance on Cameron Green's fitness for the first Test, and could affect whether Beau Webster remains in the side as a second all-rounder.
Green sent down eight overs in the first innings in Perth on Tuesday at good pace in what was his biggest bowling output in a match since before his back surgery last summer.
Webster took eight wickets for the match in Tasmania's Sheffield Shield loss to South Australia this week, but is fighting to keep his spot in the Test side.
Selectors will likely weigh up whether to play Webster in Perth as an extra bowling option, or go with Jake Weatherald as a specialist opener with Marnus Labuschagne at number three.
