The S&P 500 is getting a refresh later this month that may prove market moving as it plays out.

Index providers S&P Dow Jones Indices and MSCI are officially creating a new communication-services sector to replace telecom, the smallest of the index’s 11 segments. S&P will complete its reclassification Sept. 21, and many others who use the classifications will do so by Sept. 28. Some companies that are currently in the tech and consumer-discretionary sectors will move into the communication group.

As...