Air raid sirens sounded in three communities - Sderot, Ibim and Kibbutz Or HaNer - as the rocket was launched. Two women in Sderot were treated for shock after the rocket strike.
The IDF said it was investigating the incident, which came after two Palestinian teens were reported killed in clashes along the border fence earlier in the day.
Palestinian medical officials in Gaza named the dead as Khaled Al-Rabai, 14, and Ali Al-Ashqar, 17. Seventy protesters were wounded, 38 of them by live fire during the protests, the officials said.
The IDF said that troops guarding the border were faced with more than 6,000 demonstrators "especially violent" protests at several points along the fence.
It said the demonstrators hurled "a large amount of explosive devices, grenades and firebombs" and damaged parts of the fence.
The army also detained two Palestinians who crossed the frontier into Israel.
Protesters have staged 18 months of weekly demonstrations dubbed the "March of Return", calling for an end to a security blockade imposed on Gaza by Israel and Egypt, and for Palestinians to have the right to return to land from which their families fled or were forced to flee during Israel's founding in 1948.
Israel rejects any such return, saying that would mean an end to the Jewish state.