Three days of negotiations failed to find a compromise on the council, where the United States has regularly used its veto power as a permanent member to block measures condemning Israel.
US ambassador John Negroponte said the "one-sided, unbalanced resolution" was "silent about the terrorist atrocities committed by Hamas."
The vote on the 15-nation council was 11 in favour and the United States against, with three abstentions.
The US veto spiking the resolution brought a sharp reaction from Algeria, which said the UN Security Council is "not sending the right message to the world."
Shaikh Yasin, the 67-year-old wheel-chair bound founder of Hamas, was killed by an Israeli air strike in the dawn of 22 March as he returned from a mosque after prayers in the Gaza Strip.
Israel later claimed the assassination had been carried out and supervised by its Prime Minister Ariel Sharon. It accused Shaikh Yasin of masterminding "terror."
Though much of the world was outraged by the assassination and condemned the extra-judicial killing, the United States supported its long-time ally Israel.
The White House condoned the killing, claiming "Israel had the right to defend itself."