The state of New York sued Exxon Mobil Corp. on Wednesday, accusing the oil giant of misleading investors about the risks that climate-change regulations pose to its business.

The lawsuit, filed in state Supreme Court in Manhattan, said that for years Exxon told its investors that it adequately accounted for greenhouse-gas regulations by applying a so-called proxy cost—an estimate of the effects of future events such as climate regulations—to its business planning and investment decisions. In reality, Exxon applied either...