A photo of Kate being injected on Friday was posted on the Kensington Palace Twitter account on Saturday, May 29.
In an accompanying message the duchess said: "Yesterday I received my first dose of the Covid-19 vaccine at London's Science Museum.
"I'm hugely grateful to everyone who is playing a part in the rollout - thank you for everything you are doing."
Kate, 39, wearing a face mask, white vest top and jeans, was pictured receiving a jab in her left arm.
Responding to the Kensington Palace tweet, Health Secretary Matt Hancock, who was also jabbed at the Science Museum, said: "In the last fortnight more than half of all people in their 30s have been vaccinated.
"Delighted HRH The Duchess of Cambridge was able to get her jab at the Science Museum."
It comes after the Duke of Cambridge received his own first jab from NHS staff at the Science Museum earlier this month.
William had previously spoken in favour of the vaccine and hailed the "monumental" success of the Covid-19 jab programme.
The duke contracted Covid-19 last spring and was able to carry on with telephone and online engagements while he was treated by royal doctors but was reportedly hit "pretty hard" by the virus and at one stage struggled to breathe.
The Queen and Prince of Wales are among other members of the royal family to be vaccinated as the rollout of jabs reaches millions of people across the country.
A total of 53,842,037 Covid-19 vaccinations took place in England between December 8 and May 28, according to NHS England data, including first and second doses, which is a rise of 555,477 on the previous day.
NHS England said 32,683,816 were the first dose of a vaccine, a rise of 174,622 on the previous day, while 21,158,221 were a second dose, an increase of 380,855.
In England and Scotland people aged 30 are being encouraged to get inoculated against coronavirus.
The Covid-19 vaccination programme in Northern Ireland has opened for everyone aged 18 and over, while in Wales the invite is similarly open to all people over the age of 18.