A Romanian housewife named Rifca Stanescu, who is now 25, claims that she became a mother at age 12, and that her daughter, Maria, had a baby boy at an even earlier age, 11.
It's also worth mentioning that at age 27, husband Lionel Laiu is a pretty young grandpa as well. Read more about this very young family here.
In case you were wondering, no, this will not be a Guinness World Record. Guinness representatives have stated that they do not offer "youngest grandmother" as a category. This may be because recognition of an activity by the Guinness World Records can be seen as an endorsement of that activity. They probably do not want to publicly endorse 11 and 12-year-olds having babies.
According to this official Guinness rejection letter (albeit for a different attempted record) Guinness creates categories for activities in which they believe there is actual competition, and that by rejecting certain categories they can not be associated with the activity in the proposal and cannot be seen as endorsing it.