The newsreader is facing an internal investigation by the broadcaster after partying with nine other people at private members venue the Century Club in London’s Soho on Saturday night.
On Tuesday, her daily breakfast show was presented by stand-in Sarah Hewson.
Burley tweeted: “Evening everyone I want to apologise to you all for an error of judgment. On Saturday night I was enjoying my 60th birthday at a Covid compliant restaurant. I am embarrassed to say that later in the evening I inadvertently broke the rules.
“I had been waiting for a taxi at 11pm to get home. Desperate for the loo I briefly popped into another restaurant to spend a penny. I can only apologise.”
According to The Sun newspaper, Burley’s guests included colleagues Beth Rigby, Inzamam Rashid and Sam Washington, with the party split into two smaller groups – a table of six and a table of four.
The celebrations are said to have moved to restaurant Folie, just a few streets away.
Due to infection rates of COVID-19, London is currently under Tier 2 government restrictions – which state people cannot socialise with anyone outside their household indoors.
Socialising outdoors in a public place or garden in restricted to ‘the rule of six’.
As a journalist Burley has addressed the issue of senior government figures breaking lockdown restrictions on Sky News.
Watch: Kay Burley grills minister on lockdown restrictions
While questioning health secretary Matt Hancock about government Professor Neil Ferguson's forced resignation for breaking lockdown to meet his lover, Burley asked: "What did you think when you read it? Did you bang your head on the desk?"
A Sky News spokesperson said: “We place the highest importance on complying with the government guidelines on COVID, and we expect all our people to comply.
“We were disappointed to learn that a small number of Sky News staff may have engaged in activity that breached the guidelines.
"Although this took place at a social event in personal time, we expect all our people to follow the rules that are in place for everyone. An internal process is under way to review the conduct of the people involved.”
Last weekend it was revealed singer and The Masked Singer judge Rita Ora broke England’s lockdown rules to celebrate her birthday at a west London restaurant with celebrity pals including Cara and Poppy Delevingne and Vas Morgan, leading to a hefty fine and a public apology.
Watch: Rita Ora has apologised for breaking the rules to celebrate her birthday