"The members are meeting to look at the government's request. A decision will be made today," said Lerato Mataung, the tribunal's registrar.
Massmart's shareholders in January approved Wal-Mart's $2.5-billion (1.87-billion-euro) offer for a 51 percent stake in the company, amid concerns of worker rights by labour unions.
That was a scaled-down proposal from the world's largest retailer, which had initially offered $4.2 billion for a total buyout.
The Competition Tribunal, South Africa's top anti-trust authority, had planned four days of hearings starting Tuesday.
Labour unions have voiced concern over the bid, arguing that the giant retailer, which is known for cheap prices, would undermine local firms.
"We will tell the Competition Tribunal that we believe it is not in the best interest of South Africa for Wal-Mart to be allowed into our country," said Bones Skulu, general secretary of the South Africa Commercial, Catering and Allied Workers Union.
The union wants the tribunal to ensure that Wal-Mart upholds protections for local workers and suppliers.