Hundreds of demonstrators surrounded a police post in the small town of Madfouna, injuring at least four police officers.
A Reuters news agency photographer at the scene said Bedouin had looted the post and set several fires.
On Monday, police opened fire on a vehicle driven by “two Bedouin suspects” who they say ignored orders to stop. One was killed and the other wounded.
The dead man was identified as a drug dealer by the state news agency MENA, although the tribesmen deny that allegation.
The 250km Egyptian-Israeli border has become a major transit route for migrants, asylum-seekers and drug smugglers, with some Bedouin involved in the trafficking.
The Bedouin inhabitants of the Sinai peninsula have repeatedly complained that they are subjected to regular searches and harassment by security officials, and that police regularly arrest tribesman.
Relations between the Egyptian authorities and Bedouin have always been strained, but deteriorated futher following a spate of bombings at popular tourist destinations in the region between 2004 and 2006.
Police blamed the attacks on a group of Bedouin and thousands of tribesmen were subsequently arrested.
Around 200,000 formerly nomadic Bedouin live in northern Sinai.
The Egyptian authorities have regularly promised to pump resources into impoverished northern Sinai, which has one of the country’s highest unemployment rate.