The announcement was made Sunday on the Web site of Anncol, a news organization with alleged ties to the Revolutionary Armed Forces of Colombia, or FARC, Colombia Reports said.
FARC said "from today on we ban the practice" of "the retention of people ... in order to finance our struggle."
The group said it is not ending its armed war with the Colombian government but will use "other forms of funding and political pressure."
Colombian President Juan Manuel Santos said in a Twitter post the announcement was a step in "the right direction."
The rebel group, which has been fighting the Colombian government since 1964, has been funded by drug trafficking, extortion and kidnapping, the news Web site said.