The Securities and Exchange Commission is investigating the listings of Slack Technologies Inc. and other major companies on the New York Stock Exchange, in a probe looking at how trading was handled on the first day, people familiar with the situation said.

SEC enforcement staff have recently sent letters including one seeking information from electronic-trading firm Citadel Securities LLC related to how it opened Slack’s stock for trading on June 20 in the workplace-messaging app’s so-called direct listing, the people said....