The Federal Communications Commission on Wednesday said it plans to fine AT&T Inc. $100 million for allegedly deceiving millions of smartphone customers about unlimited wireless data plans.

The FCC alleges AT&T sold consumers data plans advertised as unlimited, then capped data speeds for those subscribers after they used five gigabytes of data within a billing cycle. Those capped speeds, the agency said, were more than 20 times slower than the normal network speeds advertised by AT&T, and hurt consumers’ ability...