The announcement by Ali Abdullah Saleh comes days before presidential and municipal elections.
"They [attackers] were targeting security, stability and development in this country. Had they succeeded in [hitting] their target, that would have been a great economic crisis," Saleh told a campaign rally on Saturday.
Saleh said the bounty would go to any civilian who helps capture a "terrorist" or any security officer who arrests or kills one.
Hours after the announcement, authorities said security forces have broken up an al-Qaeda-linked cell connected to Friday's foiled attacks.
Rshad al-Alimi, the interior minister, told reporters security forces arrested four suspects and seized explosives that the group were planning to use in attacks in the capital, Sanaa.
Four bombers were killed when security forces blew up four rigged cars at dawn on Friday before they reached the oil and gas facilities in the eastern provinces of Marib and Hadarmout that they were targeting.
The oil ministry said there was no damage to the state-owned facilities.
Saleh said that the attacks were deliberately timed to coincide with the elections to be held on Wednesday and that "they targeted the democratic feast Yemen is living".
Diplomats say powerful tribal leaders in mountain areas that are outside government control give shelter to militants, some of whom fought Soviet forces in Afghanistan in the 1980s.
Al-Qaeda and other groups see Western-allied governments such as Yemen's as traitors and therefore legitimate targets.
There was no immediate claim of responsibility for the failed attacks, but a Yemeni official has said the attackers had been identified without giving further details.
Yemen, a minor oil producer, is the ancestral home of the family of al-Qaeda's Saudi-born leader, Osama bin Laden.
The US embassy in Sanaa has asked Americans not to leave their residences and said non-essential official visits to Yemen were suspended.
Yemen, which has been battling militancy for years, has also increased security around foreign embassies and other foreign buildings after the attacks.
The foiled attacks were the first on an oil target in Yemen since the 2002 bombing of the French oil supertanker Limburg off the coast, for which al-Qaeda claimed responsibility.