The university said it had agreed with Public Health England, Devon County Council and Exeter City Council to ask students "to take significant additional measures to stop the spread of infection" between students, and to prevent transmission to the wider community.
Such a move was "necessary for us all to avoid further local restrictions, of the type already seen in a number of other universities", it added.
The only exceptions are:
When students are attending educational sessions on campus
When they are working or volunteering
When they are taking part in an organised sporting session
If they are required to support a vulnerable member of the community
In the case of an emergency where you and others are in danger
The restrictions would be kept "under regular review", it added.
Outside the current household, students should also "observe the Rule of Six and all other social distancing measures at all times".
An online groceries service was to open for students who were self-isolating or quarantining in self-catered halls "should you need to order basic provisions to be delivered to your block", it said.
Dr Virginia Pearson, Director of Public Health Devon, said Exeter's cases were "contained" and remained "predominantly in the student population and centred around a small number of households in a small area of the city".
A Devon coastal community which was united in opposition to new clifftop housing has been won round after two villagers decided to try and negotiate with the developers directly.
There were more than 100 objections to the £3m plan to knock down an old hotel in Hope Cove and build new holiday accommodation in its place.
During the tension, two locals living next to the site decided to try and start a positive dialogue.
One of them, Brian Clavin said the developers listened to him and made major concessions.
It's historically an 'us and them' approach. Reaching out to the developer for a grown-up conversation reduces the confrontational nature of property development and perhaps creates a sense of community.