Ms Stratton, who took on the role of Downing Street Press Secretary last November, is self-isolating for a period of 10 days, Express.co.uk understands.
Health Secretary Matt Hancock went into self-isolation earlier this week after coming into close contact with someone who has tested positive for coronavirus.
He said he was alerted by the NHS app on Monday evening, having led a Downing Street press conference.
Mr Hancock must quarantine despite having tested positive for Covid-19 in March, announcing his diagnosis shortly after Mr Johnson revealed his own.
It is understood that the Health Secretary was given the duration of his isolation period by the NHS app.
The health service’s website says the isolation period includes the day the individual was last in contact with the person who tested positive and the next 10 full days.
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