Detectives said the people were arrested at addresses across the city of Birmingham on Wednesday on "suspicion of the commission, preparation or instigation of acts of terrorism".
"As a precautionary measure we will have an enhanced police presence at these locations," West Midlands police said.
The government said the arrests were part of a nationwide operation.
Güncelleme Tarihi: 20 Eylül 2018, 18:16
"We can confirm that a major counter-terrorism operation took place earlier today led by West Midlands police," the Home Office said in a statement.
"The home secretary was fully briefed on the operation and is receiving regular updates as developments occur.
"This operation is a reminder of the real and serious nature of the terrorist threat we face."
Britain is on its second-highest threat level of "severe" which indicates that security services believe a terrorist attack is highly likely.
Last year, the head of MI5, Britain's domestic intelligence service, said that about 30 alleged terrorism plots were being investigated and agents were monitoring about 1,600 suspects.