A Hamas military position near Khan Younis, also in southern Gaza, was hit, witnesses said. The Israeli army had earlier told residents to leave the area.
Ehud Barak, Israel's defence minister, said at a security conference in Herzliya: "I suggest Hamas doesn't fool around with us.
"The air force is operating in Gaza as we speak. We promised calm in the south and we will keep our promise."
The rocket fired earlier from the Gaza Strip into Ashkelon damaged several cars.
The missile is the first to land in Ashkelon since Israel and Hamas, which has de facto control of Gaza, announced separate ceasefires on January 17 and January 18 respectively.
More than 1,300 Palestinians, at least a third of whom were women and children, were killed in Israel's war on Gaza, which had the stated aim of preventing rocket attacks into Israel.
Thirteen Israelis, including three civilians, died during the 22-day conflict.