The victim – named locally as Lilia Djairine – was reported to be “seriously injured” when officers were called to the scene in Uxbridge Road, Ealing, by paramedics at around lunchtime on Thursday.
An air ambulance crew also attended, but Ms Djairine – believed to be in her 20s – was pronounced dead at 12.50pm.
Officers set up a police cordon around the pizza restaurant L’oro di Napoli, which was still in place in the evening.
While police arrested a 28-year-old man at the scene, the death is currently being treated as unexplained.
Residents told the Get West London that the road would have been busy at the time of the incident.
Liz Jenner told the local newspaper the death happened “in broad daylight”.
“I’m afraid that the whole community must be shocked to the core after hearing this very sad news,” she said.
The suspect remains in custody at a north London police station and a post mortem will take place on Friday, with formal identification of the victim also to take place.
Her next-of-kin have been informed, as have the Met’s homicide and major crime command team, and enquiries are ongoing, police said.
The death comes amid a surge in violent crime in the capital, with around 81 people suspected to have been deliberately killed since the start of the year.
But despite the arrest, police have not yet launched a murder investigation in relation to Ms Djairine’s death.
:: Anyone with information is requested to call 101, quoting reference CAD 3314/19 July, or Crimestoppers anonymously on 0800 555 111. You can also tweet information to police via @MetCC