The rockets, which were fired from the Gaza Strip by Palestinian terrorists, caused no damage or injury when they struck in open fields near the Sha'ar Hanegev Regional Council, the Jerusalem Post reported.
Funeral services for Sharon, who died Saturday, had ended a short time before at his Negev ranch near the Gaza border.
Israel had increased security for the service, which was attended by many international dignitaries.
Israeli security forces said they had "made clear" to Hamas authorities in Gaza they should prevent any rocket fire during the service.
Sharon's farm had been hit in the past by missiles launched from Gaza. An Iron Dome rocket interceptor had been stationed at the farm during the service.