The Labour leader was said to have tested negative on Wednesday morning ahead of his appearance in Parliament where he grilled Boris Johnson over his isolation policy.
It will be the fourth time Sir Keir has had to enter quarantine since the pandemic began and will force him to alter plans to launch his “safer communities” campaign on Thursday.
Sir Keir said: “This lunchtime, one of my children tested positive for Covid.
“I know it’s my responsibility to follow the rules – my family and I are now self-isolating.”
A spokesman for the Labour leader said: “Keir was already doing daily tests and tested negative this morning. He will continue to take daily tests.”
Just after midday, Sir Keir accused the Prime Minister of ushering in a “summer of chaos”, criticising the confusion caused by his policy for self-isolation as Covid-19 cases soar.
Mr Johnson responded virtually via a screen in the Commons while in isolation at his country retreat, Chequers, following contact with Covid-positive health secretary Sajid Javid.
Sir Keir’s statement announcing that it was his “responsibility to follow the rules” will doubtless be contrasted with the Prime Minister’s own approach over the weekend.
Mr Johnson and Chancellor Rishi Sunak initially tried to get around quarantine after being contacted by NHS Test and Trace by saying they would join a daily workplace testing programme.
But they were forced to back down on the plans and enter isolation amid widespread public anger that they would be free while tens of thousands of people are forced to miss work or school over coronavirus contacts.
Addressing the television screen in the Commons chamber on Wednesday, Sir Keir accused Mr Johnson of having tried to “dodge” quarantine.
The Labour leader had been due to head to Wolverhampton on Thursday as part of a drive to win back support from voters.
It comes as it was reported a further 73 people had died within 28 days of a positive test in the UK and another 44,104 cases were recorded, according to the latest government figures.