The pandemic hit the Gulf state hard last year, both through the shock of low oil prices and the huge toll it took on vital non-oil economic sectors such as tourism.
The concerns of a third COVID-19 wave in Europe is weighing down on demand expectations thus negatively affecting energy prices and oil prices which are particularly sensitive in the Gulf region.
Saudi Arabia's benchmark index fell 0.3%, pressured by a 4.2% fall in Riyad Bank, which went ex-dividend.
Dubai's main share index closed 0.7% higher, with blue-chip developer Emaar Properties and Dubai Investments, the Gulf-based diversified investment group, both advancing 2.5% each.
Saudi Arabia's benchmark index eased 0.2%, hit by a 1.2% fall in Al Rajhi Bank and a 1.1% increase in Samba Financial Group.
Qatar enters another year of its blockade by Saudi Arabia, Egypt, UAE and Bahrain on accusations of backing "terrorist" groups, charges which Doha denies.