The operation in south-east England was not linked with the arrest of a 27-year-old man with knives near the Houses of Parliament earlier in the day, the Scotland Yard said.
"During the operation, a female, who is one of the subjects of the investigation, was shot by police. The woman, aged in her twenties, has been taken to hospital by London Ambulance Service. She remains in hospital in a serious but stable condition. Due to her condition, she has not been arrested at this time and remains under police guard at hospital," a Metropolitan Police statement said.
All four have been arrested on suspicion of the commission, preparation and instigation of terrorist acts under Section 41 of the UK Terrorism Act 2000.
They remain in custody at a south London Police station.
The address and persons connected with it had been under observation by counter-terrorism officers as part of an ongoing intelligence-led operation, according to the police.
There are no other reported injuries and searches at the address are ongoing, as well as further searches at linked addresses across London.
Earlier yesterday, armed officers were seen arresting a man near Parliament Square. Knives were seen lying nearby. The 27-year-old has been detained on terrorism charges and is believed to have a British passport but was born outside the UK.
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