Televison footage showed the parachutist gliding towards the edge of the crowd and colliding with people as he hit the ground.
The wounded were carried away on stretchers, with one woman appearing to have a bloodied neck.
Israel is marking its 60th anniverversary on Thursday. Festivities in Tel Aviv included naval parades, air force fly overs and the parachute jump.
In the occupied West Bank, Palestinians were also marking the six decades since what they call the "Naqba" or catastrophe.
About 700,000 Palestinians fled or were driven out of their homes during the setting up of the Israeli state.
Many of them were marching on Thursday for the right to return to the homes that they left in 1948.