TRENTON—Marijuana for medicinal purposes won't be available in New Jersey until the end of the year at the earliest, officials predicted to The Wall Street Journal, nearly three years after the state legalized the substance for the severely ill.

New Jersey—one of 16 states plus Washington, D.C., that allow medical marijuana—has taken longer than expected to launch its program because opposition to dispensaries in towns and villages was more vigorous than anticipated, and setting up a highly regulated system with safeguards...