Influential trader Keith Gill, also known as Roaring Kitty, recently sparked meme-stock rallies that sent shares of GameStop Corp. and AMC Entertainment Holdings Inc. skyrocketing. But his trading activities have also caught the attention of the commonwealth of Massachusetts securities regulator. 

“The securities division is looking into his activities,” a spokesperson for Massachusetts Secretary of State Bill Galvin told MarketWatch. “There’s not much more I can say at this point,” the spokesperson added, noting that the...