The series was filming its second season when the incident happened.
In a statement, HBO said it was “with heartbreak” that it was ceasing “all future production” on Luck.
Produced by Michael Mann and David Milch, the series looks at the seedy side of life in US horse-racing.
It sees Dustin Hoffman play a crime kingpin scheming to gain control of a racetrack and introduce casino gambling.
Luck debuted in the US in January and will see its first season finale broadcast on 25 March.
It is currently being shown in the UK on the Sky Atlantic channel.
“It is with heartbreak that executive producers David Milch and Michael Mann together with HBO have decided to cease all future production on the series <<Luck>>,” HBO said in its statement.
“While we maintained the highest safety standards possible, accidents unfortunately happen and it is impossible to guarantee they won’t in the future. Accordingly, we have reached this difficult decision.”
On Tuesday the American Humane Association (AHA) issued the suspension order, pending a “thorough and comprehensive investigation”.
HBO said the horse was being led to a stable by a groom when it reared and fell back, suffering a head injury.
The animal was put down at the track in suburban Arcadia, California, where Luck was filming.
On Tuesday, California Horse Racing Board vet Dr. Gary Beck said he had just examined the horse as part of routine health and safety procedures before it was to race later in the day.
“The horse was on her way back to the stall when she reared, flipped over backwards, and struck her head on the ground,” Dr. Gary Beck said in a statement.
A second vet determined that euthanasia was appropriate, he added.
Dr. Rick Arthur, medical director of the state racing board, said such injuries occurred in stable areas every year and were more common than thought.
During filming of the first series in 2010 and 2011, two horses were hurt during racing scenes and were subsequently put down.
The AHA called for a production halt at the Santa Anita Racetrack after the second horse’s death, and racing resumed in February after new protocols were put in place.
The first two horse deaths drew criticism from animal rights group PETA, which said the safety guidelines were “clearly inadequate” as they failed to prevent the deaths.
On Tuesday, PETA vice-president Kathy Guillermo said: “Three horses have now died and all the evidence we have gathered points to sloppy oversight, the use of unfit, injured horses, and disregard for the treatment of thoroughbreds.”
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