Saudi officials said he would meet Crown Prince Abd Allah bin Abd al-Aziz Al Saud to discuss the row which both governments said they wanted to resolve amicably.
Saudi Arabia, battling a wave of violence blamed on Usama bin Ladin's al-Qaida network, says the barrier will curb the flow of militants and weapons across its porous frontier with Yemen.
But Arab diplomats say Yemen argues the fence violates an agreement signed by the two Arab states in 2000 to end a long-standing dispute over the exact line of the border.
The accord stipulated a 20km grazing zone for livestock be established along both sides of the border and no barracks be set up in that area which would allow mobilisation of military forces.
"Our brothers in (Saudi Arabia) have the right to take all the measures they deem suitable to protect their borders and
security and to establish such a fence as long as it is outside the 20km zone identified in the pact," Yemen's state-owned weekly newspaper September 26 said in an editorial last month.
The head of Saudi Arabia's border guard Tilal Anqawi said last week the barrier, a raised, concrete-filled pipeline which he called a security "screen", was being built on Saudi soil, but did not specify exactly where.
Saudi denies crisis
He also dismissed comparisons in some Yemeni opposition newspapers between the Saudi barrier and Israel's barrier through the West Bank, which Arab states have condemned.
The new al-Wadia border outpost
between Saudi Arabia and Yemen
"What is being constructed inside our borders with Yemen is a sort of screen ... which aims to prevent infiltration and smuggling," Anqawi told Asharq al-Awsat newspaper. It does not resemble a wall in any way."
Both governments have played down the dispute. Saudi Foreign Minister Saud al-Faisal bin Abd al-Aziz Al Saud last week denied any crisis with Yemen about the border.
Diplomats say Saudi Arabia is urgently stepping up border controls after the surge of militancy last year, fuelled by weapons smuggled across desert or mountain borders with its neighbours.
The frontier with Yemen, which cuts in part through mountainous tribal regions, is of particular concern because of the widespread availability of arms in areas where central
government control remains weak.