The number of cases in the last week was 7.5 per 100,000 while the previous week this figure was 3.7.
While the number of cases is still low the increase is the 25th largest nationwide, leading to the plea.
Residents should wash their hands frequently for at least twenty seconds, use hand sanitiser when out and about and keep 2m apart from anyone they don't live with.
If it's not possible to keep 2m apart, for example in shops, they should wear a mask and face away from others to reduce the risk of transmission.
Businesses should complete a covid-secure risk assessment and make sure there are measures in place to protect staff and customers.
Cllr Seb Lowe, Leader of Rugby Borough Council, said: "Throughout this pandemic the number of cases within the borough has remained relatively low and we have seen good compliance with the social distancing measures.
"The number of cases is still low but it is concerning that we have seen an increase in the last week.
"By following the guidelines we can all control the virus and protect each other from harm.
"I would urge every resident to take precautions and do what is right for Rugby."