A photo of Kate being injected on Friday was posted on the Kensington Palace Twitter account on Saturday afternoon.
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.
More than 32 million people have been vaccinated with a first dose in England, almost three-quarters of the total adult population, while more than 20 million people have had both doses.
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.
Research shows that the Pfizer and AstraZeneca jabs are effective against the Indian variant of concern that is spreading throughout the UK.
The deputy chair of the Joint Committee on Vaccination and Immunisation (JCVI) has said that people should be “very concerned” about the Indian variant but “reassured” by the scale of the vaccine rollout
Professor Anthony Harnden told BBC Breakfast that the variant was “clearly more transmissible”.
“We need to be reassured that we’re in a very different position now in that we’ve got a highly vaccinated population and we just need to continue moving at speed,” he said.
“We do know that with this particular variant you do need two doses to offer complete protection, and so we’re very, very keen to make sure that all those, particularly higher risk groups, that’s the over-50s and those with underlying illness, receive their second vaccination as soon as feasible.”
He said people had been “very surprised” by how “quite staggeringly effective” Covid vaccines had been in prevent severe illness.