"This reckless event — in which horses are routinely killed — must come to an end," the former "Baywatch" star writes in a letter to Alison Redford.
"It's clear there's nothing that can make these races safe. The chuckwagon races must be eliminated once and for all."
Three horses died and a fourth was injured during a race at the Stampede last week.
Anderson says that, as a Canadian, she's "ashamed" that the races continue even as horses die.
"Can I please hear that you'll use your influence to convince Stampede organizers to do the right thing and permanently end these spectacles?"
A spokeswoman for Redford said Monday the premier hadn't seen the letter.
"It would be inappropriate for the premier to 'use her influence' to convince an independent organization do anything. We have the utmost confidence in the Calgary Humane Society and the Alberta SPCA, who monitor animals and events during the Stampede and enforce the Animal Protection Act if necessary," said the premier's press secretary, Kim Misik, in an email.
"We would suggest Ms. Anderson contact Calgary Stampede officials to discuss her concerns and get more information."
Anderson is best known for her bikini-clad character C.J. Parker in "Baywatch" in the 1990s and as a model for "Playboy."
In recent years, she has become an advocate for animal rights and is a member of People for the Ethical Treatment of Animals.
At the chuckwagon race last Thursday, one of the horses pulling a rig driven by Chad Harden collapsed when a major blood vessel ruptured in its abdomen — a condition the Stampede's chief veterinarian said could not have been foreseen.
Two other horses were hurt so badly in the ensuing crash they had to be euthanized on the track. Another horse needed surgery and is expected to survive.
The Stampede introduced changes last year aimed at making chuckwagon races safer for both horses and competitors. The move came after six horses died in 2010.
All horses are now inspected by veterinarians when the animals arrive at the Stampede and before and after every race. There is also a mandatory rest day after every four days of racing.
The number of outriders that accompany each chuckwagon as it thunders around a dirt track was reduced to two from four to try to avoid congestion. Several riders have been seriously injured over the years.
Anderson is not the first celebrity to speak out against the Stampede this year.
Bob Barker, retired host of popular game show "The Price is Right," has said he wants to see an end to the rodeo.
"I would like very much to see them celebrate the 100th anniversary of the Calgary Stampede by saying that is enough animal cruelty,'' Barker said in an interview with The Canadian Press before the Stampede's centennial celebrations kicked off.
"Let's wind it up and close it down."
The 10-day Stampede wrapped up Sunday after 1.4 million visitors walked through the turnstiles. That broke the previous record by almost 147,00 people.
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