The furry explorer climbed inside the child's plaything and jammed its head through a small hole at the rear.
Despite its owners attempts to free it, the plastic proved too tough and the "unusual" emergency call-out was made.
Oxfordshire Fire and Rescue Service said the kitten was unharmed but its experience served as a warning against "diving into your presents too early".
Crews were called to a house in Stanford-in-the-Vale at about midday on Wednesday.

The woman, whose surname is Yang, lived in a padlocked 10-sq-metre cell and slept on a wooden bench, says Southern Morning Post.
Suggestions that she may have been there voluntarily have sparked debate about whether anyone will be held to account.
In recent months, online users have been up in arms over a number of cases of where elderly people have seemingly been neglected by their children.
Yang's conditions were exposed by a local woman, "Pretty Nan Gualan", who posted a video of Yang sitting by a cage door on the popular video service Miaopai.
"How could you make her live in here?" she asked of the woman's captors, "And not give her food?"
The video has been watched more than 1.8m times since it was uploaded on 6 January, and many viewers have taken to popular microblog Sina Weibo to voice their outrage.
Tens of thousands posted using the hashtag #92YearOldKeptInPigsty, calling Yang's son and daughter-in-law "beasts" and "scum" and calling for some form of "retribution".
There was further anger after Southern Morning Post posted pictures on 10 January showing her malnourished body during a medical check.
The paper says the local hospital is now treating Yang and residents in the area have helped by providing bedding and clothes.
Many say they are relieved that she is receiving help. In 2014, a 90-year-old woman in central Henan province died after being subjected to similar conditions.
But Southern Morning Post reports that the woman's son, surnamed Wu, says his mum volunteered to move into the cage because her incontinence had "given them a great burden and she was worried about making the house smell".
Police say Wu and his wife are suspected of maltreatment, but if it turns out that Yang moved in voluntarily, they would be unlikely to face charges.
Yang's case is not the first to ignite anger.
In recent months, similar stories have highlighted the apparent neglect of elderly Chinese people by their children and have created a stir on social media.
In November, tens of thousands of online users reacted angrily to a video from Henan province, which showed a 62-year-old man picking up rubbish and eating restaurant leftovers by choice, so as not to be a burden at home to his middle-aged daughter.
The same month, social media users discussed the case of a 70-year-old woman in Jinan, northern Shandong, who was selling vegetables throughout the night in sub-zero conditions to help her son save money to buy a house.
One user, "Keetop", said it showed "how abnormal society has become".
BBC Monitoring reports and analyses news from TV, radio, web and print media around the world. You can follow BBC Monitoring on Twitter and Facebook.
A three-month old kitten had to be rescued by firefighters after it got stuck in a toy car.
[NEXT_CONCEPT]
Images of an emaciated elderly woman have rattled Chinese social media users, after papers in the southern Guangxi region reported that the 92-year-old had been kept in a pigsty by her son and daughter-in-law "for years".