Mr Biden said there would be "enormous consequences" for the world if Russia made a move on the nation, which sits on its south-western border.
His comments came as other Western leaders repeated warnings that Russia would pay a heavy price for invasion.
Russia has accused the US and others of "escalating tensions" over the issue and denies it plans to enter Ukraine.
However, Moscow has built up troops at the border, with some 100,000 Russian soldiers deployed in the region.
Taking questions from reporters, Mr Biden replied "yes" when asked whether he could see himself imposing sanctions on the Russian president personally the event of an invasion.
He said such a move across Ukraine's border would mean "enormous consequences worldwide" and could amount to "the largest invasion since World War Two".
Mr Biden added that he would feel obliged to beef up Nato's presence in eastern Europe.
"We have to make it clear that there's no reason for anyone, any member of Nato, to worry whether... Nato would come to their defence," he said.
But he repeated that there were no plans to send US troops to Ukraine itself.