Carrie’s mum had now formed a household bubble with her daughter's young family.
Johnson, 56, and Symonds, 32, became the first unmarried couple to occupy Downing Street when they moved in during July 2019.
After announcing their engagement last February last year, Wilfred was born on April 29 at University College Hospital, London.
Under lockdown rules, people can form a support bubble with another household of any size if they live by themselves or if their household includes a child who was aged one or under.
A spokesman for Johnson declined to comment on the claims reported in the Sunday Telegraph.
A spokesman for Symonds said she "declined to comment on private arrangements, given Carrie’s mother is a private individual".
Symonds was born in London in 1988 when her mother was a lawyer at the Independent newspaper, which her dad Matthew Symonds co-founded.
The official coronavirus death toll in the UK has risen to more than 80,000 as lab-confirmed cases passed the three million mark.
It comes as doctors have warned that pressure on the NHS could get worse in the coming weeks and some experts criticised the current lockdown measures as not being strict enough.
The number of patients with Covid-19 in hospital is also at a record high in England, and medics have warned the full impact of social mixing over the Christmas period has not yet been seen.
The Government has doubled down on its "stay at home" message by launching a new advert, fronted by England's chief medical officer Professor Chris Whitty, urging everyone in England to "act like you've got" coronavirus.
Boris Johnson and Carrie Symonds praise NHS staff for saving PM's life and delivering son in first joint TV appearance