The paceman, who was only in the T20I squad, was struck on the left index finger by a net bowler this week.
Cricket Australia confirmed ahead of the opener in the three-match T20I series in Colombo on Tuesday that Abbott will not be replaced in the squad.
Abbott was due to link up with Australia’s A squad in Sri Lanka after the T20I series. Scott Boland has been called up to cover for Abbott in the A team’s four-day matches ahead of the two-match Test series
Meanwhile, Peter Handscomb will leave the A squad to return to Melbourne and be with his pregnant wife.
Jimmy Peirson has been added to the squad as a replacement for Handscomb.
Alex Carey is set to captain the Australia A team in their first 50-over match in Colombo on Wednesday after being added to the squad along with Cameron Green, who will also play.
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