Work taking place will include replacing the track on Ridgeway Road, between Manor Top and Hollinsend tram stops.
Repair work will also take place on Park Grange Road to fix the concrete surfacing and sealant around the rails.
Several tram stops including Granville Road, Park Grange Croft, Park Grange, Arbourthorne Road, Spring Lane, Manor Top, Hollinsend, Herdings/Leighton Road and Herdings Park will not be in use between 28 July and 15 August.
No services will run on the purple route during the work.
A tram replacement bus service will run between Fitzalan Square in the city centre and Herdings Park, via Gleadless Townend, up to every 15 minutes, serving all the affected tram stops.
Timetable changes to the blue route mean trams will run between Halfway and Gleadless Townend every 15 minutes while the upgrades are carried out.
A SYMCA spokesperson said: “We have successfully completed work recently on sections of track in Birley, Hillsborough, Gleadless and Langsett Road.
“By investing in the Supertram system, we’re increasing the longevity of the region’s tram network and ensuring the safe operation of this popular service for the millions of people who use it every year.”