Since her father’s inauguration in September, Ms Ruto has held several high-profile events and meetings under the title.
In Kenyan law, no such office exists.
Many Kenyans online have been expressing anger over her engagements, and asking who is funding them.
Some have described her as a “low budget version of Ivanka [Trump]”, who regularly attended political functions while her father Donald Trump was US president.
Some have nicknamed her Quickmart Ivanka – referencing a low-cost Kenyan supermarket.
But Ms Ruto doesn’t seem to be too upset and tweeted a video of herself smiling, while walking around the grocery chain.
Ms Ruto has been meeting leaders across the country and attending international forums with foreign dignitaries since her father William became president.
In one video being shared widely online Ms Ruto is seen speaking to an audience at a summit in Tanzania where she introduces her “team from Kenya” including her adviser and another who is the “head of trade and investments at the Office of the First Daughter”.
The audience appear to respond loudly with claps and some laughter.
“I don’t get what is funny,” Ms Ruto responds as she attempts to continue with the introductions.
She became one of the top Twitter trends in Kenya on Wednesday as people asked whether she was using taxpayers’ money.
She responded with a statement saying: “The Office of the First Daughter is a private entity. It is neither a constitutional office nor is it being funded by the Kenyan taxpayer.”
She goes on to explains that her “office” has an “independent structure and facilitators” and praises its “objectives of championing youth based agendas and climate change advocacy”.
Communications strategist Mark Bichachi told the BBC: “If it’s a private entity, why call it that? Use a private name, it’s tied to her father being president.”
While political commentator Daisy Amdany said Ms Ruto was “within her rights” to do whatever she wants but warned that she needed to be careful about the image she is portraying: “It offends the public that her father ran on [a] platform of ending dynasties and it looks like they want to establish dynasties, I don’t think it’s okay.
Mr Ruto won the August election against Raila Odinga, the son of a former vice-president, who was backed by the outgoing president Uhuru Kenyatta, himself the son of Kenya’s first leader.
“She probably means well, but it doesn’t come across well,” Ms Amdany continued.
Ms Ruto herself has said that some of the comments about her were “hurtful” but that she knows she is doing the right thing in trying to help Kenya’s youth.