The 27-year-old is a UK national.
She had just arrived on a moody from the Ethiopian collateral of Addis Ababa when she was arrested on Friday.
Police pronounced she had been taken to a south London police station, where she stays in custody.
In a statement, police said: “Officers from the Met’s opposite terrorism authority have arrested a 27-year-old lady at Heathrow Airport.
“The woman, a UK national, arrived on a moody from Addis Ababa and was arrested on guess of credentials of militant acts under territory 5 of the Terrorist Act 2006.