A statement from FARC blamed "enemies of peace" for restricting the group's online presence.
"This latest attack from the enemies of peace and of the Colombian population comes from the right, who are worried by the growing interest and discussion which these peace talks are creating in different sectors of Colombian society," the statement reads.
FARC has asked its followers to send a message to Facebook to demand the re-establishment of the group's page.
Facebook has not commented on the blocked account, Colombia Reports said.
The blocking of the Facebook page comes just weeks after the group's blog, which was hosted on a Google server, was taken down.