Iran, the third largest OPEC member, immediately denounced the Gulf states' actions. Qatar has positioned itself as an intermediary between Iran and other Gulf nations.
It is possible Iran could quit the deal in protest, but its production has topped out around 3.8 million barrels a day. It could struggle to increase output significantly following years of sanctions imposed over its nuclear program.
Qatar is one of the world's largest exporters of natural gas and the biggest shipper of liquefied natural gas, or LNG. But with the exception of natural gas sent through a pipeline to UAE, Smith does not think Qatar's energy exports will be disrupted much because most are shipped by seaborne tankers.
"These flows should continue to the key destinations and specifically in Asia. There shouldn't be too much of a disruption on that side of things. It's only the limitations that are being applied in the region," Smith told CNBC.
Map of Qatar, source: Energy Information Administration
Applying pressure on those exports would require the Saudi-allied nations to impose some sort of blockade on Qatar. That would mark a significant escalation, especially given that Doha hosts a critical U.S. military air base.
"In our view, there are no immediate risks for regional energy security, but the breakdown does pose the risk of an intensified proxy battle in Libya and possibly may even have implications for the U.S.'s forward airbase in Qatar," RBC Capital Markets said in a research note on Monday.
Qatar and Egypt have backed opposing sides in Libya's civil conflict, which has sidelined the country's oil supply.
But RBC sees little chance that Egypt will block Qatari tankers from the Suez Canal, and believes efforts to block Doha's shipments will have only a limited effect unless the situation deteriorates further.
However, Scott Modell, managing director at energy and geopolitical risk consultancy the Rapidan Group, noted that Saudi state media on Monday issued "some really tough language suggesting naval action against Qatar."