A second member in Salazar's group, possibly his bodyguard, also was killed.
The Mexican navy said in a statement that Salazar, commander of the 8th Naval Zone, and other navy personnel were traveling on a rural road in the northwestern part of the state when the gunmen opened fire on their vehicle.
The Times said the news website Milenio reported three suspects were taken into custody.
President Enrique Pena Nieto sent in military units into Michoacan state in May to restore government control of the area, where vigilante groups had formed to fight back against a drug cartel called the Knights Templar, the Times said.
Last week, four federal police officers were killed and several others were wounded in response to the government crackdown, the newspaper said.
Federal officials said at least 20 criminals were killed in gunbattles with authorities.