The Yemeni interior ministry in a statement said the gunmen had attempted to attack the installations in four cars packed with explosives.
Aljazeera's correspondent in Yemen said two refineries, in Marab and Hadramut, had been singled out for attack.
The four attackers and one security guard were killed in the incident, the interior ministry said.
Friday's early morning attacks occurred 35 minutes apart, directed at a Yemeni oil refinery in the northeast province of Marab and a Canadian-Yemeni oil storage facility at the Dubba Port in Hadramut province - scene of a 2002 attack on the French tanker Limburg.
The four men, two at each target, were dressed in uniforms similar to those worn by staff at the facilities and had timed their attacks to coincide with early morning shift changes, security officials said.
Exchange of fire
A security official in Marab said two suicide bombers drove towards the refinery and one attacker engaged security guards before his car exploded.
The second car blew up moments later.
An official in Hadramut said one of two suicide bombers drove through the main gate and opened fire on the guards, killing one, as a second car tried to advance behind it.
The guards returned fire and the two cars exploded, the official said.
A interior ministry statement said an investigation was under way to determine the identity of the "terrorist elements" behind the attacks.
The attempted attack comes just days after Ayman al-Zawahiri, Osama bin Laden's deputy, said that the Gulf and Israel would be the next targets of al-Qaeda, in a video message on Monday coinciding with the fifth anniversary of the September 11 attacks on the United States.
Yemen is the ancestral homeland of bin Laden and in October 2000, 17 US sailors died when suicide bombers aboard a small boat attacked the destroyer USS Cole off the southern port of Adan in an attack acknowledged by al-Qaeda network.
Yemen has pledged to crack down on attacks by al-Qaeda-linked militants and kidnappings by tribesmen.
Yemen is due to hold presidential and municipal elections on September 20.