Police found a golden Volvo parked in the middle of the suspension bridge heading to Thon Buri at 5.55pm.
Documents in the car indicated the owner was Pan Puengsujarit, the deputy secretary general of Matubhum party and former deputy spokesman of the Prime Minister's Office.
Eye witnesses said they saw the driver get out of the car and jump into the Chao Phraya River.
The police are conducting a search for the body in the river.
Gen Sonthi Boonyaratglin, leader of Matubhum party, said Mr Pan's son had confirmed his father was missing and that he had health problems.
A native of Uttaradit, Mr Pan was deputy speaker of the Prime Minister's Office in 1997 and 2000 when Chuan Leekpai was prime minister.
Prior to that, he was a history lecturer at Srinakharinwirot University's Phitsanulok campus and later at Prasarnmit campus in Bangkok.
He ran in several elections under the Rassadon and Pheu Pan Din banners.
He ran as a party-list MP in the 2011 election under the Matubhum banner but the party won only one seat in the House.
Later, he was appointed deputy secretary general of the party.