The allrounder, who had been due to play the T20 Blast, is heading home after just one game
He had been due to take a full part in the T20 Blast which begins next week but will now return home immediately to begin his recovery ahead of Australian season.
“Sean’s injury is incredibly unfortunate as he made a great impression during his first game and had already become a popular member of the dressing room,” Alec Stewart, Surrey’s director of cricket, said.
Abbott, who was part of various Australia squads during last season and played in the T20I and ODI series against India, was not included in the preliminary group named for the tour of West Indies next month.
As with anyone returning to Australia he will have to undergo two weeks quarantine and will then have around three months to recover before the beginning of the domestic season with New South Wales.
Abbott is the second Australian to have a county deal cut short by injury following Billy Stanlake who suffered a stress fracture of his back after one game for Derbyshire.