The Cathedral, known as St Philip's, on Colmore Row, announced the closure in a statement on its website on Wednesday.
The Cathedral's Acting Dean, Canon Nigel Hand told Premier's News Hour the Church already had a policy in place "put together with advice from counter-terrorism" detailing what to do if the threat level was raised to critical as it was back in 2007.
"[The policy states] that we should shut and then reassess, which is exactly what we are going to do," he said.
He rejected the idea that the decision to close was done in fear and said: "The decision up to now has been with a heavy heart, I don't think it's anything that most of us want to do but if you have a policy you need to adhere to that policy."
Activity outside the church however is permitted and the dean said there is still an opportunity for people to continue to gather in the square outside the church to "pray, to light candles, to meet together, to be still, to think".
He said many are still doing so.
It is the first time the cathedral has closed in response to a threat level but the dean insisted that there was no intelligence that the Cathedral could be a target
Listen to Canon Nigel Hand speaking with Premier's Marcus Jones:
