The index, which is produced by Swedbank and the purchasing managers' organization Silf, rose from 53.8 in August to 57.7 in September, a level that has not been recorded in over three years.
"The service sector has had difficulty establishing itself in the growth zone but now shows signs of a clear recovery, even if the September result should not be overinterpreted", writes Jörgen Kennemar, economist at Swedbank, in a press release.
An index above 50 indicates growth.