WASHINGTON—Education Secretary Betsy DeVos is planning to repeal an Obama-era rule that aimed to penalize for-profit colleges that leave their students with unreasonable debt and poor job prospects, according to people familiar with the plan.

The Obama administration drafted the rule, known as the “gainful employment” provision, to crack down on career-education schools, many of which operate as for-profits, if students graduate without meaningful job opportunities and with debts they cannot pay off.

Administration...