The protester was identified as Aaron Bushnell, 25, an Air Force service member. He is reported to have died from his wounds.
The Netherlands added extra security at the Israeli embassy in The Hague on Thursday following a threat.
The national bomb squad is on its way to investigate the object, the spokesperson said.
The circumstances of the incident are under investigation by New Delhi police alongside Israeli security forces.
Several pro-Palestinian demonstrations have been held outside Israeli embassies around the world in recent weeks, including in Tokyo, in protest against Israel.
Four people aged between 17 and 21 found in the area were remanded on suspicion of attempting to destroy property with explosives, possession and use of explosive materials and carrying a weapon.
The US embassy said it is back to normal operations on Wednesday afternoon.
The suspect was a foreign worker, aged 53, who was engaged in a small commodities business in Beijing, local police said in a statement, and an investigation was underway.
To date, only five countries have opened Jerusalem embassies: the United States, Honduras, Guatemala, Kosovo and Papa New Guinea.
Latin American countries move their embassies to Jerusalem to appeal to voters, for religious reasons, or to score points with the US
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