The exact target is not known but the embassy said the "potential imminent terrorist attack" threatened the busy Bole district, which includes the capital's international airport and several diplomatic missions.
"The embassy has received threat reports of Al-Shebab's intent to target the Bole area," said the notice to citizens released yesterday.
"Restaurants, hotels, bars, places of worship, supermarkets, and shopping malls in the Bole area should be avoided until further notice, because they are possible targets."
The embassy warned its citizens in Addis Ababa "to avoid large crowds and places where both Ethiopians and Westerners frequent".
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The Shebab, which carried out the September 2013 massacre in the Kenyan capital Nairobi's Westgate mall, continue to pose a regional threat, including plotting or carrying out attacks in Djibouti, Ethiopia, Kenya and Uganda, as well as inside Somalia.
The Al-Qaeda-affiliated Shebab have lost a string of key towns and ports in recent months to 22,000-strong AU force, which fights alongside government troops.
However, Maman Sidikou, who heads the AU mission in Somalia, told the UN Security Council in a briefing yesterday the Shebab have managed to "still retain appreciable numbers of its fighters and equipment.