Footage of Mary Bale throwing four-year-old tabby Lola into a bin sparked an angry online campaign, with some animal lovers calling for her death on social networking site Facebook.
It also led to an investigation by the RSPCA, which plans to interview Ms Bale later today.
In a statement released to the media this afternoon, Ms Bale, 45, said: "I want to take this opportunity to apologise profusely for the upset and distress that my actions have caused.
"I cannot explain why I did this, it is completely out of character and I certainly did not intend to cause any distress to Lola or her owners."
The bank worker, from the Stoke area of Coventry, added: "It was a split second of misjudgment that has got completely out of control.
"I am due to meet with the RSPCA and police to discuss this matter further and will co-operate fully with their investigations.
"I wish to reiterate that I am profoundly sorry for my actions and wish to resolve this matter to everyone's satisfaction as soon as possible."
Ms Bale's apology came after police revealed they were "closely monitoring" online threats to her.
Hundreds of people posted angry messages on Facebook after a clip showing Lola being thrown into the green rubbish bin was uploaded by her owners.
A spokeswoman for the social networking site said the group, entitled Death to Mary Bale, contravened Facebook's terms of use.
Some used the site to publish Ms Bale's address, while others called for her to be violently punished. One Facebook user said she should be "repeatedly head butted", while another wrote: "She should be flogged to within an inch of her life, the evil b****."
A Facebook spokeswoman said: "We can't comment on individual cases for privacy reasons but I can tell you that one group, entitled Death to Mary Bale, has been removed today."
The spokeswoman said Facebook users were encouraged to report offensive comments posted on the site, adding that moderators would remove anything deemed to be a "credible threat".
West Midlands Police described some of the group's content as "inflammatory and offensive".
A spokeswoman said: "We have monitored Facebook to assess any threat of harm to Mary Bale as part of this investigation.
"The investigation is being led by the RSPCA but obviously the other strand of this now is Mary Bale's safety and we are looking at the potential impact of these messages.
"I would not go so far as to say we are investigating death threats, that is not the situation, but we are closely monitoring these groups and messages."
She added: "There are no plans to give any kind of formal police protection but we are talking to Mary Bale about her personal safety, we are having that conversation with her, and we do want to make sure she is ok."
Lola's owners, Stephanie and Darryl Mann, of Bray's Lane in Coventry, said they were "stunned" by the reaction to the footage, taken from security cameras outside their home.
The couple urged people to let the RSPCA and the police deal with Ms Bale and "not take matters into their own hands".
In the clip, Ms Bale is seen stroking the cat before picking it up by the scruff of the neck and dumping it in the bin.
Lola, who was trapped for 15 hours, emerged unscathed and is said to be fully recovered from the ordeal.
Speaking to The Sun, Ms Bale said she noticed the cat as she was walking home from work and began stroking it.
She said: "I don't know what came over me, but I suddenly thought it would be funny to put it in the wheelie bin which was right beside me.
"I did it as a joke because I thought it would be funny. I never thought it would be trapped. I expected it to wriggle free."
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