Ben-Gvir, the security minister, and Smotrich, the finance minister, will face a travel ban and asset freeze.
The UK and other Western nations are increasing pressure on Israel's government amid the Gaza war; Foreign Secretary David Lammy said the two senior Israelis had incited "serious abuses of Palestinian human rights".
Israeli foreign affairs minister Gideon Sa'ar called the sanctions against the elected officials "outrageous".
Smotrich and Ben-Gvir, members of right-wing parties, have been criticised for their hardline stance on the war, with Smotrich opposing aid to Gaza and Ben-Gvir advocating for resettlement of Gaza's population.
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