In the seven days between 4-10 June - the most recent figures available - there were 83 new cases, a 167 per cent increase on the previous week.
More than half of the positive cases were of people under the age of 30, with 30.7 per cent aged 19 and under and 22 per cent between 20-29. Meanwhile, 5.7 per cent of cases were in people over the age of 70, showing a slight increase in the rate of cases in the older population.
Shropshire Council said it was working alongside Public Health England to minimise the spread.
A spokesman said: "With Delta variant cases rising rapidly across the UK, it was expected that we would see an increase in Shropshire too.
"However, the infection rate is still below the national and regional averages and for the second week running, there has been no Covid-19 related deaths in our local hospitals.
During the seven-day period between 4-10 June the infection rate for Shropshire was 25.7 per 100,000 people.
It was 55.7 for the West Midlands and 78.3 for England.
Two hospital beds were occupied by Covid-19 patients.
Shropshire Council has reminded people that anyone over the age of 18 can now book their Covid vaccination
"There are plenty of vaccines and appointments available in Shropshire so please book online as soon as possible or call 119," the spokesman said.
The government has set a new target to have offered a first dose to all adults by 19 July and a second dose to two-thirds of the over-40s.
Figures for the area covered by Telford & Wrekin Council are published separately.