Jamie's Italian in Princesshay is expected to shut in the next few months, along with five others around the country.
The vote to leave the EU is being blamed.
The chain's chief executive says it is "a tough market", which has become even harder post-Brexit.
The closures will affect 120 staff nationally, but the company says it will try to find them work in other parts of the business.
Raw sewage pours into landmark Devon river
Storm overflows gush into waterway for 40 per cent of year
Work underway to return shingle to East Devon beach
Bulldozer in action for Storm Goretti clean up
Car park fees increase at Devon beauty spot
Northam Burrows season ticket to rise
Tank shell shut downs recycling centre
No one was hurt
Exeter's Royal Clarence hotel to be restored
'Progress is moving fast'
