The 160-year-old company famous for its trenchcoats and cashmere scarves said the mainland China market had returned to growth but performance was weighed by Hong Kong and Macau.
Retail revenue grew by 1 percent to 603 million pounds ($869.53 million) helped by strong demand in Europe.
Like-for-like sales were unchanged year on year, an improvement from a 4 percent fall in the second quarter.
The results were in line with analysts' expectations, helping to ease concerns over a slowdown in the luxury sector, which has been hurt by a fall in Chinese buying.
Burberry reported a sharp sales slowdown in Hong Kong and China in October, leading the FTSE 100 company to miss sales growth forecasts and warn of an increasingly challenging environment for luxury goods.
Other luxury groups that expanded rapidly in mainland China such as Gucci and LVMH have also suffered from the economic uncertainty there, and violent stock market gyrations this year have not helped.
Chinese shoppers in Hong Kong and mainland China account for between 30 and 40 percent of Burberry's global revenue.
The company is expected to report a full-year pretax profit of 428 million pounds, down from 455.8 million in the previous year.