Josh Inglis, who was dropped for the rapid-fire Boxing Day Test, will also return to the BBL and play for Perth, ahead of the fifth and final Ashes Test.
After their BBL matches, both players will rejoin the Australia squad in Sydney to prepare for the New Year's Test at the SCG, starting on January 4.
After playing seven Tests this year, Webster was left out of the Australia XI for the opening match of the Ashes in Perth and has been unable to get back into the team.
But he appears a genuine chance to reclaim his spot due to Cameron Green's repeated failures with the bat this series.
Green's position is under major threat after averaging just 18.66 with the bat in the first four Tests of the Ashes.
After running himself out on day one in Melbourne, Green again threw his wicket away in the second innings.
The 26-year-old tried to guide a Ben Stokes ball away into the off-side, but was caught at second slip.
Inglis is less likely to earn a recall after having a top score of 32 in his three innings during the Brisbane and Adelaide Tests.
Webster will be available to play for the Hurricanes in their BBL match against the Melbourne Renegades on Monday.
Inglis is expected to line up for the Perth Scorchers in their clash with the Sydney Thunder at ENGIE Stadium on Tuesday night.
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