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Canada's Denis Shapovalov struck the ball in anger and hit Gabas during his game with Kyle Edmund, defaulting the match to hand the tie to Great Britain.
The International Tennis Federation said the 17-year-old's actions were "unintentional" but  fined him £5,600.
The ITF says the surgery was successful and Gabas is now recovering at home.
The Davis Cup World Group first-round tie in Ottawa was poised at 2-2, with Edmund leading 6-3 6-4 2-1 in the final match, but Canada's hopes ended when Shapovalov was disqualified.
He later apologised to Frenchman Gabas in the match referee's office and said he was "incredibly ashamed and embarrassed".
Gabas went to Ottawa General Hospital as a precaution, but no damage to the cornea or retina was found. On his return to France he had an X-ray, which revealed a fracture of the orbital bone under his left eye.
"I am now concentrating on rest and rehabilitation so I can be back on court in the near future," said Gabas.
Umpire Arnaud Gabas has had surgery to repair a fractured eye socket after he was hit with a ball during Britain's Davis Cup win over Canada last week.