The group's statement was emailed to the media.
It said: "This forewarning is to ensure that civilians avoid milling around oil pipelines and installations or close to military checkpoints and vehicles to minimise civilian loss of life."
Mend has carried out a campaign against oil installations over the past two years. The campaign has reduced Nigeria's oil output by about a fifth and added to worldwide oil price rises.
Nigeria is Africa's largest crude oil exporter.
The Nigerian army said that troops would not be sent out on to the streets and that it was used to such threats.
However, Sagir Musa, spokesman for the military task force in the Niger Delta, said that law and order would be maintained.
"I can assure you of the readiness of our troops to deal with any situation."
Some private contractors have said they will employ additional security in light of the threat.
Mend and several other groups in the Niger Delta demand local state control of the region's oil wealth.
Yar'Adua took power on May 29 last year.
He has attempted to appease rebel groups by freeing three opposition leaders and drawing up plans for talks.
However, progress on any deal has not occurred.
When Henry Okah, a suspected Mend leader, was arrested in September on arms procurement charges the group reneged on a unilateral ceasefire it had made shortly after Yar'Adua became president.
Okah is currently on trial on treason and terrorism charges and his release is a pre-condition for a permanent settlement.
Yet, the past release of regional Mend leaders has not led to a cessation of attacks by the group.