The UAE Foreign Ministry did not immediately respond to an email seeking comment.
Algiers said it was giving the UAE ambassador to Algeria 48 hours "to comply with the decision".
Algerian media outlets have in the past sharply criticised the UAE, accusing it of seeking to sow regional discord.
Last year, Algerian President said his country's relations with all Gulf states were warm except for one, in a thinly veiled reference to the UAE. He described ties with , , and as "brotherly", while accusing the unnamed country of meddling in Algeria's internal affairs and seeking to destabilise it.
Tensions escalated further in February, when Algeria began the process of cancelling an air services agreement with the UAE that was signed in Abu Dhabi in May 2013.
Tebboune has often referred to the UAE in speeches as a "micro-state" or "statelet" seeking to destabilise several countries in the region.
"Wherever they set foot, blood flows," he said in a televised interview in July, adding that the UAE has had a "very negative impact".
"We want them to stay away, so that blood does not flow in our country," he added.
At the time, Tebboune said a diplomatic break "would have happened long ago" had Algeria not sought to avoid "deepening divisions" in the .
(FRANCE 24 with Reuters and AFP)
