The corporation, which is politically impartial, said it will not be involved in the business group while it is registered with the Electoral Commission as a supporter of the pro-UK Better Together organsation.
It is the latest high profile organisation to be affected by last week's decision by the CBI to register with the Electoral Commission as an opponent to the SNP's policy.
The BBC's suspension will continue until after the polling day of the independence referendum, on September 18 this year.
Several organisations, including the government funded tourism body VisitScotland, and universities and Scottish Enterprise have already quit over the row.
In a statement, the BBC said: "In order to protect the BBC's neutrality, the CBI and the BBC have agreed to suspend the BBC's membership during the business group's registration period under the terms of the Scottish Referendums Act 2013."
CBI Director General John Cridland said: "In order to protect the BBC's neutrality, the CBI and the BBC have agreed to suspend its membership duringn the business group's registration period [30 May to 18 September] under the terms of the Scottish Referendum Act 2013."
The universities of Glasgow, Aberdeen and Edinburgh have already departed the business lobbying body in a development seized on by the pro-independence side.
STV and Balhousie Care Group - a company chaired by businessman and prominent Yes campaigner Tony Banks, have also quit.
They like others have said the CBI's decision to register as a campaign group with the Electoral Commission was at odds with their political neutrality.
Business for Scotland Chairman Tony Banks said: "It is now clearly not sustainable for any neutral public or private sector member with a Scottish interest to remain in the CBI by the end of this week. The legal position is clear. The CBI has behaved disingenuously and been exposed. They are now facing the consequences.
"The CBI is nothing more than a wing of the No Campaign and membership fees have been spent on No vote campaigning against the interests of Scottish democracy. All members of the CBI, anywhere in the UK and particularly if they receive public funding, should now, at the very least, be seen to ask serious questions even if we already know the answers."