Jo Smith, 16, found her sister Hannah's body last week. Hannah, 14, apparently became the target of Internet trolls after she sought information about eczema on the site Ask.fm.
Jo said she has received nasty messages on a tribute page to Hannah on Facebook and on her own Facebook page, the Daily Mirror reported.
"I've just lost my sister and now I've got to deal with getting abuse myself. These trolls don't care what happened to Hannah or what we're going through, they just live in their sad little worlds," she said. "It's really upsetting. I'm struggling to cope with what's happened and don't need these trolls hounding me."
David Smith, a truck driver who lives in Lutterworth, Leicestershire, said the abuse aimed at his daughters "defies belief."
Smith called on Prime Minister David Cameron to find ways to curb websites where cyberbullying is common. Ask.fm is based in Latvia, which might make controlling it difficult.