The episode saw Jon host segments of the programme from a primary school in Abergavenny, Wales to celebrate the launch of the UK's biggest children's writing competition, 500 Words.
During the show, Jon was joined by Hacker The Dog and while many viewers loved seeing the iconic children's puppet make an appearance, one person wasn't impressed.
They wrote on X: "Why have a rude stuffed puppet on in front of children?"
Jon was quick to respond to the comment, quipping: "But having Hacker was ok?", alongside a winking emoji.
Fans took to the comments section to praise Jon for his reply, with one person writing: "Touche @jonkay01. I loved the piece with Sir Lenny in the Palace," while another dropped a GIF showing a woman spitting out her drink with laughter.
Many viewers, however, praised Hacker's appearance on the programme and were keen to see more of the puppet.
One person wrote on X: "We need more Hacker on BBC Breakfast!" while another added: "Watching BBC Breakfast and seeing Hacker causing chaos like always," dropping a laughing emoji.
A third person tweeted: "Might start a petition so Hacker T Dog can be a permanent presenter."
Elsewhere in the episode, a prerecorded clip showed Jon and Sir Lenny Henry, one of the judges of the writing competition, make a trip to Buckingham Palace, where the final will be held next year.
The duo sat down for afternoon tea and Jon gave Lenny a poem written by Queen Camilla, asking him to tell viewers how to enter the competition.
The royal signed off the letter with the words: "The hunt is on. We seek a star. The best of luck – Camilla R."
The writing competition, which was first launched by radio host Chris Evans in 2011, encourages children aged 5-7 and 8-11 to send in stories for a chance to win a host of prizes. The finalists will receive a £20 National Book Token, while bronze, silver and gold winners of each age group will have their stories read by celebrities.
For more information, visit the BBC website.
Tuesday's programme isn't the first time in recent weeks that Jon has left the studio for a new location.
At the beginning of September, Jon swapped Salford's Media City for Langstone Harbour in Hampshire for a special edition of the show, which delved into the issue of sewage pollution along the coastline and in our waterways.
Following the broadcast, Jon shared a heartwarming tribute to his colleagues, whom he called a "talented, professional and lovely bunch".
"I'm unbelievably lucky to work with such a talented, professional and lovely bunch at #bbcbreakfast," he wrote on Instagram.
"This morning's outside broadcast in #Portsmouth was a huge technical and editorial challenge…We had to deal with some complex politics and new BBC data about sewage and water pollution - while also making the most of a beautiful sunny morning in #LangstoneHarbour," he added, before giving out special mentions to members of his team, including "amazing" weather presenter Carol Kirkwood.