The Briton broke a bone in his left hand following a crash in first practice ahead of last weekend's Monaco E-Prix, having hit the barrier into Sainte Devote.
The injury took place to the same hand which Bird broke during the 2022 London E-Prix and which kept him out of the season finale in Seoul while he underwent surgery and recovery.
After being assessed in Monaco, where it was confirmed Bird had again broken a bone in his left hand, he travelled back to the UK and underwent a successful surgery earlier this week with the team confirming he can "now look forward to a speedy recovery and a return to racing soon".
Team principal Ian James said: "We’re very pleased to report positive progress on Sam’s recovery, with a successful operation on his hand supporting his journey back into the car.
"Taylor did a stellar job in his last-minute call-up in Monaco, as did the team, who provided him with great support and guidance throughout.
"He will now be able to build on that experience, while Sam works on his recovery – with the team’s full support.
"We’re looking forward to having Sam back in the car soon."
At the age of 19, Barnard became the youngest starter of a Formula E race when he competed in last Saturday’s Monaco E-Prix, having only been told 20 minutes before the second practice session that he would be replacing Bird.
Having only done one 30-minute session before qualifying, where he finished last in his group but only 1.730s off the leading time, Barnard put in an assured drive to eventually finish 14th out of 20 finishers.
The Briton, who currently competes in Formula 2 this season, admitted that there was not enough time to worry about making his Formula E debut in Monaco, such was the short notice he was given.
Barnard was set to compete in the rookie test following the Berlin E-Prix double-header on 13 May, but will now be unable to do so, with McLaren yet to confirm either of its two drivers.
