Eight rockets were fired from Gaza and four fell into Sderot settlement.
Footage of the attack shows the rocket impacted near a playground packed with dozens of children and there are reports that there was not enough room in bomb shelters.
The footage was released by the Israeli Defence Force (IDF) and shows one rocket explode midair, but then a huge explosion causes mass panic and screams from school children.
Military and Defence Correspondent for the Jerusalem Post, Anna Ahronheim said: “A 34-year-old is in light to moderate condition with wounds from glass shards and a 20-year-old in a light condition with injuries to limbs.
“Another eight suffering from stress, including two pregnant women.”
Two homes in Sderot were also reportedly hit by the shrapnel and several cars were damaged.
According to the IDF, the rockets were launched from the Hamas-run enclave and two were intercepted by the Iron Dome missile defence system.
The IDF said: “Terrorists shot at civilian vehicles that were being used in the effort to construct the barrier around the security fence in the northern Gaza Strip. One vehicle was hit.”
Israeli Prime Minister Benjamin Netanyahu, Defence Minister Lieberman and IDF senior officials are currently holding a situational assessment at the IDF HQ in Tel Aviv.
There are also reports that the Israeli Air Force (IAF) has carried out drone strike on multiple locations in Gaza, but this is unconfirmed.
Palestinian media claim that a building belonging to the Hamas naval force was struck.
The rocket fire came from Gaza shortly after an IDF tank struck Hamas posts in Gaza after hots were fired across the border towards civilian engineering vehicles working on the IDF’s underground barrier with the coastal enclave.
In a statement, the IDF said: “Terrorists shot at civilian vehicles that were being used in the effort to construct the barrier around the security fence in the northern Gaza Strip. One vehicle was hit.”
The IDF closed several roads near the Gaza border earlier on Wednesday after warning it was concerned of a retaliation from Hamas after two of its elite members were killed in an IDF strike on Tuesday.
The rocket fire also comes as a senior Hamas official said UN and Egyptian mediated ceasefire talks between the terror group and Israel have reached “advanced stages” and a deal was expected to be signed soon.
Deputy Hamas chief in Gaza, Khalil Al-Hayya, told Al Jazeera television: “We can say that actions led by the United Nations and Egypt are in advanced stages and we hope it could yield some good from them.
“What is required is for calm to be restored along the border between us and the Zionist enemy (Israel).”