Officers were called to Swinfield Close in Feltham at 7.12pm on Monday amid concerns over the pair’s safety.
The Metropolitan Police said the boy remains in a critical condition, while the woman’s injuries are not life threatening.
An air ambulance took the pair to a nearby hospital for treatment.
One witness told Sky News: “I heard a lot of screaming and crying, it was quite distressing to hear. It’s a family, they’re new to the area, they’ve not long moved in.”
A crime scene has been established and an investigation is under way.
Detectives believe “the parties involved were known to each other”.
Police are currently trying to trace a man who was known to reside at the address where the knife attack took place.
More from UK
‘Hammer-wielding thieves’ target Michael McIntyre as he picks up son from school
RBS stake sale realises £2bn loss on bailout value
Motorists ‘charged through the nozzle’ for fuel
Two men due in court over murders of gangland pair Paul Massey and John Kinsella
Free refill scheme along Wales coast path to fight plastic pollution
Teenager, Safaa Boular, found guilty of first all-female UK terror plot
No arrests have been made.
Anyone with information is asked to contact Hounslow Police on 101 or tweet @MetCC quoting CAD 6981/4June, or call Crimestoppers on 0800 555 111.