The city is expecting the government to implement tougher measures later this week but is already asking people not to mix indoors with others from different households.
Alison Challenger, the director of public health for Nottingham, said: "We are seeing a dramatic increase in COVID-19 cases in Nottingham. Our rate of infection is now rising higher than many other parts of the country.
"This is a significant and worrying change."
The infections follow the movement of students across the country as they travelled to cities to start a new university term.
Manchester's two main universities - Manchester University and Manchester Metropolitan University - have also suspended all in-person teaching for the rest of October.
A few courses that rely on practical training will be exempted.
In a joint statement, the universities told the Manchester Evening News they met with public health authorities and Manchester City Council following a "significant increase in the number of COVID cases across the city of Manchester".
They added: "Our campuses remain open and we will continue to ensure the necessary safety precautions are in place to make any activity on campus as safe as possible. We will continue to support our staff and students."
The University of Nottingham is running its own testing programme on its campuses, and puts its high number of cases down to that scheme.
It said 106 students in university halls had tested positive, with 93 in other purpose built accommodation. Some 226 students living in private accommodation have contracted the virus, while eight staff members are also included in the data.
There are 35,000 students and 10,000 staff at the Midlands institution.
Officials in Nottingham have told local media that they are worried about a significant rise in cases in the city and are working with Public Health England (PHE) to supress the spread.
At the University of Sheffield, as of Monday, 583 students have tested positive for COVID-19 - as have six staff members.
The university said that when it is notified of confirmed cases, it uses timetabling data to identify close contacts and encourages them to go into self-isolation.
Those in quarantine are supported by the university and receive regular welfare checks and help with food deliveries.
The university is home to 29,000 students and around 8,000 staff members.
Sheffield's infection rate has shot up to 286.6 over recent days as a result of the sharp increase in cases.
Some 283 pupils and 35 staff at a school in Cardiff have also been told to self-isolate after 11 of them tested positive.
The headteacher of Ysgol Gyfun Gymraeg Plasmawr told parents in a letter that at least two pupils and three members of staff were among those who had the virus.
The school is reducing the size of its contact bubbles and reinforcing infection control over the next few weeks.