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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.

The 26-year-old finished a career-best second in his Ford Fiesta in the French round in October, his second podium of the season.
Evans is seventh in the Championship standings but his future is unclear.
"We will see what comes and will look with what happens next year afterwards," he said.
"There has been a lot of chat about it [my future], but really to be honest nothing has changed.
"At the beginning of the year I wasn't in a position with a contract for next year anyway.
"There has been a lot of speculation, I don't see how one rally can change everything, but for sure we want to do our best for myself and the team and it's the team's home event."
M-Sport managing director Malcolm Wilson has yet to make a decision on his drivers for next year, with Evans' current deal expiring at the end of 2015.
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But Wilson admitted that a good result in the Wales Rally GB will help the Welshhman when the team hold contract talks at the end of the World Rally Championship.
"I am not making a decision on drivers until after this event but in real terms if he has a great result here then that will help, but ultimately that's not going to be the final decision," said Wilson.
"There is a lot of other stuff going on that is related to the whole business, and that is why I have not been making  a decision, but it's not to say I am not  going to have Elfyn in the team next year,.
"But we have got so much other stuff going on behind the scenes and the programme being extended to extra events - it is how we work out the resources."
Dogellau-born Evans, alongside co-driver Daniel Barritt, took part in the ceremonial start in Llandudno on Thursday evening ahead of Friday's first stage.
The son of former British Rally champion Gwyndaf Evans is in his second WRC season and was fifth in last year's Wales Rally GB.
"It's been a bit of a mixed and difficult year for us but there's plenty of positives to draw from it as well," Evans added.
"We're hoping for the chance to come back and build on that next year.
"In terms of competitiveness and stage times we've come leaps and bounds but maybe the results don't quite reflect that for various reasons."
Evans is back in Wales for the final round of the World Rally Championships, which Frenchman Sebastien Ogier won for a third year running in September.
Ogier has tipped Evans and Northern Ireland's Kris Meeke to do well at Wales Rally GB, which starts in the forests of mid-Wales on Friday.
"It's always been a special event," Evans said.
"You can still enjoy it at the same time and it's a pretty strange feeling rallying at home after spending 12 rallies away all over the world.
"It feels good coming back to familiar stages and familiar conditions. We're sure to enjoy this weekend."
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.
[NEXT_CONCEPT]
World Rally Championship driver Elfyn Evans will fight for a podium at Wales Rally GB and potentially for his future with his M-Sport team.