Joseph Gillinder found the fox in the hall of his home in Bromley, Kent. Fortunately, the fox saw the dad and ran out of the house.
But it left Joseph, 31, and his partner Vix Henstock, 28, shuddering about what the consequences might have been for baby Violet had the animal not been disturbed.
The incident has echoes of a case two years ago where a fox entered through an open door and bit nine-month-old twins Isabella and Lola Koupparis sleeping upstairs in Hackney, east London.
Joseph told Parentdish: "I was taking a bin to the top of my driveway, no more than metres, and my hands were full so I didn't pull the door closed behind me. My baby was asleep upstairs and my partner was inside the house in the lounge.
"The fox snuck in behind my back within seconds. When I turned around I spotted it running into my house into the hallway and shouted straight away."
Speaking to the Evening Standard, Joseph added: "We have a very small baby in our house and that makes it not just a small problem but one of utmost concern and worry. I dread to think what one could do to a small baby."
The couple have written to Bromley council asking them to clamp down on rubbish left on the streets which attracts the animals.
Councillor Tim Stevens, who is Bromley council's representative for public safety, said: "Bromley council's approach to foxes is to discourage an increase in their population without physically harming them.
"This is achieved by advising residents to stop doing things that might encourage foxes. These include removing attractions from the garden, sealing up holes and hiding places."