Political editor Beth Rigby and correspondent Inzamam Rashid have also agreed to be off air for three months.
In a statement, Sky News said: "A small number of Sky News staff attended a social event in London on Saturday evening during which COVID-19 guidelines were breached...
"As a result of an internal review Sky News presenter Kay Burley has agreed to be off air for six months, and political editor Beth Rigby and correspondent Inzamam Rashid have agreed to be off air for three months...
"All those involved regret the incident and have apologised...
Everyone at Sky News is expected to comply with the rules and the company takes breaches like this very seriously indeed."