According to a statement released Friday, the company's action comes amid unfavorable "customer feedback" about the fee, which was scheduled to be implemented Jan. 15.
Molly Katchpole set up a petition on Change.org against the fees. Her petition gathered 95,000 names by Friday afternoon.
Katchpole is also responsible for the successful campaign that forced Bank of America to drop a monthly $5 fee for debit card use earlier this year.
Verizon, the country's largest cell phone company, hoped the fee would encourage customers to use electronic check payments, which are cheaper, and automatic credit card payments, which are more reliable.
The Associated Press contributed to this report.