Investors in American Outdoor Brands Corp. on Tuesday won a shareholder vote urging the top U.S. firearm maker to do more to address gun violence.

The proposal asks the maker of Smith & Wesson guns to track shootings involving their products and consider investing more in technology to prevent their unauthorized use. Nearly 70% of investors in Sturm, Ruger & Co. backed a similar shareholder proposal at that company in May.

The...