South Yorkshire Police say a woman in her 30s has been arrested following Nyla May Bradshaw's death.
The former US ambassador was given a security clearance despite concerns being raised during checks.
Young people are to be offered the MenB vaccine after three cases of meningitis were confirmed.
It comes after a video is shared in which a group claims to have targeted the nearby Embassy of Israel.
The broadcaster was known for his eclectic taste and for helping champion world music on BBC Radio 1.