Archer will now begin a 5-day isolation period and will undergo two COVID-19 tests in this period, which have to test negative before his self-isolation period is lifted, England and Wales Cricket Board (ECB) said in an official statement.
"I am extremely sorry for what I have done," said Archer. "I have put, not only myself, but the whole team and management in danger. I fully accept the consequences of my actions, and I want to sincerely apologise to everyone in the bio-secure bubble.
"It deeply pains me to be missing the Test match, especially with the series poised. I feel like I have let both teams down, and again I am sorry," he added.
The West Indies team have been made aware of this development and are satisfied with the measures that have been imposed, informed the ECB.
England are 0-1 down in the series following their four-wicket defeat in the opening Test at the Ageas Bowl.