PdV Marina's new president is Cesar Vladimir Romero Salazar, a navy captain who also heads the national aquatics institute INEA.
The arrests were the latest manifestation of a purge spearheaded by industries minister Tareck El Aissami, who chairs a new presidential commission tasked with overhauling PdV.
PdV has been hammered by US sanctions for over a year, and today's oil price crash will only aggravate the company's troubles.
Former PdV Marina president Oswaldo Vargas, widely known as "the Scorpion", was detained in Caracas on 6 March by agents of the defense ministry's military intelligence agency (Dgcim).
Vargas is charged with leading a systematic smuggling operation that employed PdV tankers to steal fuel from terminals near the Amuay and Cardon refineries on the Paraguana peninsula.
Interior and justice minister Nelson Reverol said the arrests include 30 officers and crew of the PdV-owned products tanker Negra Hipolita flagged in Venezuela.
"This is not simply an act of diverting fuel, it is also an act of treason," Reverol said on state-owned VTV television.
Government intelligence officials used information provided by oil union leaders to track the Venezuelan-flagged tanker after it departed from anchorage near the Amuay refinery on 5 March transporting 126,000 bl of gasoline for delivery to the Venezuelan port of La Guaira.
Union officials have long complained that corrupt PdV officials were using company tankers to skim fuel during cabotage operations.
During the short voyage from Amuay to La Guaira, the tanker switched off its transponder and transshipped some of its cargo to a smaller Colombian-flagged tanker, Reverol said.
This is not the first time the Negra Hipolita has drawn attention. PdV used the tanker to ship diesel to Syria in 2011-12, when US and EU sanctions against Damascus kept most suppliers away. Last year, the tanker was among around 15 PdV vessels that came under Venezuelan army control. But the vessel is not among the tankers that have been targeted by US sanctions in recent months.
More arrests are possible as Dgcim investigates alleged theft at PdV's Bajo Grande terminal on Lake Maracaibo, the El Palito refinery terminal in Carabobo state, and the Jose and Guanta terminals in Anzoategui state, an interior ministry official said.
The arrests followed the detention of the head of PdV's lubricants unit, and two oil traders accused of spying for the US.