Saudi Arabia and its allies cut off ties with Qatar on Monday after accusing the gas-rich state of supporting extremism across the region.
On Tuesday, Saudi Foreign Minister Adel Al-Jubeir said that to rebuild relations, Doha must cut its support for "extremist" groups, including Hamas.
He said Qatar-supported Hamas, which runs the Gaza Strip, "undermines the Palestinian Authority."
In a statement on its website, Hamas said the party felt "deep regret and disapproval" at the Saudi statement.
"These statements are a shock to our Palestinian people and to our Arab and Islamic nation, which considers the Palestinian cause its central cause," the statement said.
The Islamist movement seized Gaza in a near civil war with forces loyal to Palestinian president Mahmud Abbas in 2007. The two factions have been at loggerheads ever since.
Hamas has fought three wars with Israel since 2008, and the Jewish state enforces a crippling blockade on Gaza.
Qatar has provided tens of millions of dollars for the reconstruction of Gaza since the last conflict with Israel in 2014.